Brathwaite returned figures of 4 for 18 that included the wickets of Chris Lynn, who top-scored with 56, the dangerous Joe Burns for 7, James Bazley for a duck and Mark Steketee for 2 as Brisbane were restricted to 148 all out.
Jake Ball took 3 for 25 from his too over to provide support to the giant Barbadian. Jackson Bird also weighed in with the ball taking 2 for 22.
Chasing 149 for victory, the Sixers were struggling at 54 for 4 before Captain Daniel Hughes’ 51 helped steady the ship. Hughes’s dismissal in the 17th created jitters for the Sixers. Brathwaite lost his wicket six balls later for just 2 as Sydney slipped to 130 for 6, which opened the door for Brisbane.
However, Daniel Christian’s unbeaten 38-ball 61 took the Sixers home, hitting the winning boundary off the final ball of the match with his side closing on 152 for 7.
The win put the Sixers on 25 points, two points clear of second-placed Sydney Thunder while the Hobart Hurricanes are third on 19 points.
The Heat started the day on 10 points with two games to play but vaulted into the top five with a 71-run victory clinched with 14 balls to spare at the MCG.
AB de Villiers laid the platform for the Heat with a searing 71 off just 37 balls, helping Brisbane to 186-5.
The table-topping Stars promptly collapsed in response, spinners Mitchell Swepson and Mujeeb Ur Rahman doing the damage for Brisbane as Melbourne were bowled out for 115.
DEVASTATING DE VILLIERS
Veteran De Villiers had not scored a half-century in the BBL going into Saturday's contest, but he changed that fact in emphatic fashion.
The South African cleared the rope six times, with two of his sixes coming in an expensive Clint Hinchcliffe over.
De Villiers' primary support came from Australia international Marnus Labuschagne, who finished unbeaten on a 13-ball 24, the pair combining for a fifth-wicket stand of 70.
STARS PUT IN A SPIN
Marcus Stoinis (17) got the Stars' chase off to a strong start but it proved the first of two false dawns for the Stars, who lost Stoinis and Seb Gotch to James Pattinson in the fourth over.
Peter Handscomb (27) and Nick Larkin (22) appeared to have mounted a recovery with a stand of 36, only for the former to be run out chasing two as Mujeeb and De Villiers combined in the field.
Danger man Glenn Maxwell (1) followed three balls later as he was bowled by Swepson, who struck again to remove Nic Maddinson (9) and then Larkin after Nathan Coulter-Nile had fallen to Mujeeb for a duck.
That left the Stars on 92-7 and the tail never looked like mounting a remarkable recovery.
A TIGHT FINISH
In the fight for the final two playoff places, the Heat join the Scorchers on 12 points and would qualify as it stands, with Hobart Hurricanes and Sydney Thunder each a point back with a game to play.
Perth face the Thunder in their finale, while the Hurricanes visit Adelaide Strikers and the Heat face bottom side Melbourne Renegades.
The fight for the top five is going down to the wire.
Uncertainty around international travel restrictions as De Villiers and his wife prepare for the birth of their third child played a significant role in the former South Africa batsman pulling out.
The 36-year-old scored 146 runs in six appearances in the 2019-20 BBL – the first time he had participated in the competition – as the Heat failed to qualify for the finals for the third time in succession.
De Villiers, who is currently participating in the Indian Premier League, hopes to get another chance to play for Brisbane as he feels there is "unfinished business".
"We're expecting our latest child very soon and with a young, growing family and the uncertainty around travel conditions due to COVID-19, we reluctantly decided it wasn't going to be this season," De Villiers said.
"The Heat were great to us last season and I am very open to returning to the club in future. The team didn't get the results we were hoping for and I consider there is some unfinished business to deal with."
Heat head coach Darren Lehmann added: "We've been in regular contact with AB since last season and while things initially looked fine for him to come back, there have been a few factors emerge which have changed everyone's plans.
"The main one, aside from the challenges represented by COVID-19 and international travel, is that AB and his wife Danielle are expecting their third child very soon.
"Naturally we're very pleased for them and know that the next few months will be a very special time for all."
There was some positive news for the Heat on Tuesday, however, as they announced the return of spinner Mujeeb Ur Rahman, the world number two T20I bowler, for the 2020-21 BBL.
The Big Bash League is due to start on December 3 with a clash between Adelaide Strikers and Melbourne Renegades.
Aaron Finch led a cool and commanding chase, his 63 not out leading the Renegades to 155-3 after the Heat had set a target of 155 at Docklands.
Only a win would have been enough to secure a play-off place for Darren Lehmann's side, but they failed to make the most of chances in the field, meaning the Sydney Thunder take the fifth and final spot.
With AB de Villiers (six) failing to fire after another top-order collapse, questions will likely be asked about Lehmann's future after a disappointing end to a hugely underwhelming season.
RENSHAW LEADS RESISTANCE AFTER HEAT GO OFF THE BOIL
The Heat were 1-35 after just 21 balls as they endured another miserable start after winning the bat flip.
Sam Heazlett's wild slice gave Finch an easy catch, and Ben Cutting, perhaps over-confident after four early boundaries that included two sixes off Will Sutherland (3-30), was lost lbw when teeing up for another big swing.
De Villiers went to sweep Samit Patel (1-23) only for the ball to cannon off the back leg and into the stumps, and when Chris Lynn was bowled by Nabi (1-23) for the loss of just 14, the Heat's troubles were mounting.
Renshaw and Marnus Labuschagne began the rebuilding job, the latter digging deep for 28 off 26 deliveries before Jack Wildermuth caught him trying to clear the ropes from Cameron Boyce (1-29).
Renshaw remained a beacon of resistance, his unbeaten 65 helping the Heat amass a respectable target before he was run out in the final over.
FINCH KEEPS COOL AFTER COOPER TANTRUM
Tom Cooper and Finch made an encouraging start to the chase before the former sent a delivery from Cutting (2-35) to the grateful grasp of Jack Prestwidge at deep midwicket, leaving Cooper visibly fuming as he headed back to the dugout.
The Renegades were 2-44 when Daniel Christian was caught superbly by Renshaw and, when Beau Webster was bowled full and straight by Cutting after making 14, Heat hopes were beginning to rise.
Finch, though, refused to panic. Australia's Twenty20 and ODI captain showed few signs of wilting in the Heat onslaught, with Nabi's four boundaries helping to keep the pressure off his skipper.
Prestwidge allowed a Finch drive to slide through his fingers as the Heat found their season slipping away, another mistake on the rope helping Finch bring up his half-century.
Six more over deep backward square and a drive wide of cover signalled the death knell to the Heat's play-off ambitions and gave the Renegades something to smile about at the end of a difficult season.
Chasing 165 to win at the Gabba, the Heat made a flying start and were 84-0 in the sixth over, taking full advantage of the powerplay.
However, a batting slump of bewildering proportions saw them lose 10 wickets for 36 runs to be all out for 120, with leg-spinner Cameron Boyce taking 4-15 in his four overs.
It was the worst 10-wicket collapse in Big Bash history, league officials said.
The Heat middle and lower order owed an apology to openers Sam Heazlett and Chris Lynn, who showed sizzling form. Heazlett made 56 from 37 balls, and captain Lynn was destructive as he rattled to 41 from 15 deliveries.
Marcus Harris took a fine catch on the run, just in from the ropes, to remove Lynn, who had struck three sixes in his whirlwind knock.
Brisbane still looked set to win with several overs to spare, but an hour of largely self-inflicted carnage was just getting under way.
AB de Villiers was bowled two balls later, charmed out by a fine leg break from Boyce, and when the same bowler had Matt Renshaw caught at slip from the next ball, it was the first real sign that something was stirring.
The Heat rebuilt and at 113-3, with Heazlett and Joe Burns at the crease, they looked to have seen off the storm.
It was at that point a tempest swept in, Samit Patel removing Heazlett and Jimmy Peirson with consecutive deliveries in the 13th over. Burns was run out two balls later, sent back by batting partner Ben Cutting and falling way short of his ground.
Cutting and Josh Lalor fell in the space of three balls to Dan Christian, before Boyce stepped in to complete the onslaught. Seven wickets fell for seven runs in the wild finale.
The Renegades have put up an awful title defence, losing nine in a row until finally registering a victory in their last match when scoring a Duckworth-Lewis-Stern success against the Sydney Thunder.
This was a second victory of their lamentable season, and one to savour.
Boyce said on BT Sport: "I think we were all a bit nervous after the start. That was pretty clean striking there [by Lynn and Heazlett], so it obviously needed something pretty special.
"But after the powerplay I thought we bowled pretty well as a unit. Our season hasn't gone the way we wanted it to, but we do feel we've been close in about six or seven of our games.
"It's just been one of those years. I said last week it would be nice to repay our fans a little bit.
"We've got to take a lot of momentum and confidence out of the game. They got away in those first six but we pegged them back really nicely. Hopefully we can finish the season with a couple of wins."
The Renegades earlier reached a competitive total when Mohammad Nabi and Patel lifted them from 131-6 after the 18th over to 164-6 at the end of their innings.
Beau Webster made 36 and Shaun Marsh 27, but it was Nabi's quickfire 22 and Patel's 23 from 10 balls that put pressure on Brisbane, although nobody could have envisaged the drama to come.
Renshaw tipped a big hit from Matthew Wade in the air before jumping from behind the boundary to palm the ball up for Tom Banton to take the catch.
There was a shrug of the shoulders from Renshaw, but Wade had to depart for 61 in his first match of the tournament and the Hurricanes went on to post only 126-9 at The Gabba - Josh Lalor taking 3-21.
Scott Boland claimed 3-16 to give the Hurricanes hope, yet they were comfortably beaten as Cutting made 43 not out and Jimmy Peirson an unbeaten 23 to seal victory for the Heat with 10 balls to spare.
Darren Lehmann's side are up to third after three consecutive victories, two of which have come against Hobart.
WADE DISMISSAL CAUSES A STIR
Renshaw showed great athleticism and quick thinking to set up a simple grab for Banton, but Wade's dismissal sparked a debate over the rules.
A tweet from the official Lord's and MCC account cleared up any doubts, stating: "The key moment is when he first touches the ball, which is inside the boundary. He's airborne for his second contact."
New Zealand all-rounder Jimmy Neesham was among those to call for a rule change and Wade would no doubt agree, having been sent on his way after clearing the rope twice in his first knock of the competition.
BRISBANE FEELING THE HEAT AFTER BOLAND BURST
It was very much game on after the Heat lost four wickets for only 19 runs.
Boland got rid of Max Bryant for 28 and collected a further two wickets in three balls when he had Renshaw caught behind before snaring Joe Burns later in the ninth over.
The Hurricanes were given another major lift when Chris Lynn was run out following a mix-up with Peirson, reducing the Heat to 71-5 in the 11th over.
BRISBANE CUT TO THE CHASE
Hobart were made to pay for a lack of runs, though, as Cutting and Peirson completed a successful run chase.
Cutting's best knock of the tournament and a measured innings from Peirson got Brisbane home - the pair putting on 60 for the sixth wicket.
The powerful Cutting - who also took three catches - was dropped by David Miller but the damage had already been done at that stage and he struck Thomas Rogers for a third six to end that match in emphatic fashion.
The hosts were dominant in Brisbane as James Pattinson starred with the ball, claiming a five-for as Adelaide failed to bat out their 20 overs.
Left with such a meagre total to chase, the Heat initially toiled as they lost two early wickets, but Matt Renshaw and BBL debutant AB de Villiers' 77-run partnership took the game away from the visitors.
The result moves the Heat above the Strikers and into fourth.
PATTINSON FIVE-FOR STRANGLES STRIKERS
Each of the top five Strikers batsmen fell to Pattinson, who may not have been the most economic of the bowlers, but he was certainly the most dangerous.
Having posted 0-52 on his BBL return against Perth Scorchers at the weekend, the Australian went for 33 on Tuesday but also tallied up his victims.
Jonathan Wells (14) was the only top-order batsman to make it into double figures as the Strikers fluffed their lines badly in the powerplay.
Rashid Khan's 28 down the order was the best contribution, but when Liam O'Connor was the last man out without scoring, it was clear Adelaide had come up well short of a competitive total.
DE VILLIERS AND RENSHAW GET A GRIP
Perhaps there was an element of complacency in the way the Heat set about their very modest chase.
Captain Chris Lynn went for a golden duck and Max Bryant followed him after a brisk 10 from five balls.
It needed Renshaw (52) and De Villiers to get a hold on things, with the latter falling for 40 and leaving Joe Burns (10) to come in and help finish the job with 28 balls to spare.
Hosein took 3-15 in helping restrict Brisbane Heat to 144-6 in search of Melbourne Renegades’ 166-7 from their respective 20 overs. Russell, meanwhile, smashed 35 that set up Renegades’ match-winning score.
After Brisbane Heat’s captain Jimmy Pearson won the toss and chose to field, Renegades’ openers Nic Maddinson and Sam Harper got off to a flyer scoring 65 at better than 10 runs an over before Harper was dismissed for 21 in the seventh over by James Bazley, who took 2-19 in the match.
From 65-1, Melbourne slipped to 78-4 by the 10th over before Maddinson and Russell carved out a fifth-wicket partnership of 78 before the former was dismissed by Matthew Kuhnemann in the 18th over for 87.
Hosein barely troubled the scorers and was out for one to Bazley’s final ball of the 19th that yielded only three runs as Melbourne struggled to close out on a high. Russell lost his wicket off the first ball of the 20th leaving Melbourne to limp towards their total of 166.
Kuhnemann was the best of the Brisbane bowlers with 3-32.
Hosein struck almost immediately in the Brisbane chase removing openers Josh Brown for seven and Max Brian for a duck as the Heat struggled early on 11-2 in the third over.
Russell dismissed the dangerous Sam Billings for six in the seventh over to have the Heat in further trouble at 34-3.
However, Colin Munro and Jimmy Pearson set about a recovery putting together a fourth-wicket partnership of 54 that was broken when Munro was run out for 35.
Hosein delivered another crucial blow when he bowled Pearson for 43 in the 15th over with the Heat still needing from 33 balls for victory.
Ross Whitely and Bazley added 41 for the sixth wicket but were unable to score at the required rate. Bazley was out off the final ball of the match for 19, leaving Whitely unbeaten on 28 from 18 balls.
Russell returned figures of 1-26.
The win means Melbourne Renegades is among the early leaders along with Adelaide Strikers and Sydney Thunder, each team having two points from their opening matches of the season.
Lehmann was on the Gold Coast watching his son, Jake, captain a Cricket Australia XI against the England Lions on the Gold Coast when he suffered chest pains.
The ex-Australia batsman, who turned 50 on Wednesday, is recovering in hospital and will be operated on this weekend.
Lehmann said: "I would like to thank everyone in the Australian cricket family for their concern.
"I am receiving the best of medical care and am confident I'll be back on my feet soon."
Lehmann, who has been coaching Brisbane Heat in the Big Bash League, took time out from his role as Australia coach in January 2016 after he was hospitalised with deep vein thrombosis.
Lynn hit 11 fours in his 55-ball innings along with three sixes, having pledged to donate 250 Australian dollars towards the Red Cross Bushfire Appeal for each maximum he hits during this year's tournament.
The Heat skipper was ably supported by opener Max Bryant, who provided a similarly uncompromising 65 from 36 deliveries at the top of the order.
With that 95-run stand for the second wicket having left Brisbane well placed after midway, Australia internationals Matt Renshaw (30) and Ben Cutting (18 not out) supplied breezy cameos alongside Lynn to post an imposing 212-3.
A brisk 46-run stand for the opening partnership between D'Arcy Short and Caleb Jewell fired Hobart hopes but they were playing an increasingly difficult game of catch-up after the halfway point of the innings as wickets fell regularly to stifle momentum.
The Hurricanes completed their allocation on 181-9, with the wickets shared around for Brisbane.
Medium pacers Mark Steketee and Jack Prestwidge took 2-29 and 2-16 respectively as the Heat bounced back impressively from being skittled for 109 by Perth Scorchers last time out.
They move up to fifth in the table as one of three teams on four points – a cluster completed by Hobart in seventh.
LYNNSANITY REIGNS
Man-of-the-match Lynn demanded a response after the thrashing against Perth and led from the front. This was his 33rd half-century in a format in which he thrives.
Following his 94 versus Sydney Sixers, the 29-year-old now has the two highest individual scores in this season's BBL.
FAULKNER INJURY HURTS HOBART
The Hurricanes attempts to restrict a rampant Brisbane battling line-up were compromised by James Faulkner limping off the field after bowling only half of his overs.
Why the all-rounder was then sent out to bat with a runner and face the final ball of the innings with 32 required is anyone's guess.
TWENTIES LEAVE HURRICANES ROARING WITH FRUSTRATION
In contrast to the substantive innings provided by Lynn and Bryant, Hobart's batsmen repeatedly threw things away after getting starts.
Six were dismissed between 23 and 28, including each member of the top five, without going on.
Australia international Marsh blasted an unbeaten 93 off just 41 balls to lead the Scorchers to an impressive 213-3 – their highest total in Big Bash League history.
The Perth skipper plundered 44 of his runs off 13 deliveries from Ben Laughlin, who finished with the joint-most expensive figures in a BBL match of 1-60.
Tom Banton gave the Scorchers hope with an entertaining 55, but Brisbane came up short on 179-8 and the Scorchers moved level with them on eight points.
MARSH ON THE MARCH
Josh Inglis started strongly with 28 off 14 balls and Marsh ensured the Scorchers' tempo did not drop.
The all-rounder racked up three fours and eight maximums – three of which came in succession off the final over from Laughlin.
That took his unbroken partnership with Cameron Bancroft (41 off 29) to 124 and the hosts to a tally that would always prove difficult for the Heat to chase down.
BANTON'S BRILLIANT FAREWELL
Brisbane were in with a chance while Banton was at the crease, though, as the opener another stunning display in his final appearance before being replaced by AB de Villiers.
The 21-year-old, who will join the England squad in South Africa for the three-game ODI series in February, produced a series of stunning shots, the pick of the bunch being a ramp from off stump off Jhye Richardson that landed well beyond the ropes.
Banton brought up his third fifty of the competition off 25 balls with a drive through mid-off, but he was caught and bowled by Fawad Ahmed, who did well to cling on as he trod on the non-striker's stumps.
BRISBANE FALL SHORT
Banton's dismissal at the end of the 10th over did not immediately change the complexion of the match for the Heat, who remained into the hunt thanks to the 41-run partnership between Ben Cutting (20) and Joe Burns (37).
However, the run rate slowed and the Scorchers grasped control with the ball, Richardson, Joel Paris and Chris Jordan finishing with two wickets apiece.
Captain Hayley Matthews hit her highest score of the season with 46 while Emma de Broughe hit 42 to help the Renegades post 169-7 from their 20 overs after the Heat won the toss and elected to field.
Nicola Hancock starred with the ball for Brisbane with 4-20 from her four overs while Grace Harris took 2-16 from two overs.
The Heat’s chase then fell agonizingly short of their target, reaching 167-9 from their 20 overs.
Grace Harris completed an excellent all-round performance with a top score of 65 but she was the only Brisbane batter to pass 20 with Jess Jonassen (17) and Nicol Hancock (17) both coming the closest.
Sarah Coyte took 3-26 from her four overs for the Renegades while Georgia Prestwidge was also among the wickets with 2-43 from four overs.
Matthews took 1-29 from her four overs, including taking the responsibility of bowling the last over and defending just six runs to seal the Renegades’ second win of the season.
The Renegades won the toss and elected to field first, a decision that proved costly as the Heat’s Australian opening pair of Grace Harris and Georgia Redmayne put on a mammoth 165 for the first wicket.
Harris scored a 50-ball 65 including six fours and a six while Redmayne remained unbeaten on 98 from 67 balls including 12 fours. Laura Harris was not out on eight alongside Redmayne as the Heat eventually posted 180-1 from their 20 overs. Matthews was expensive, conceding 40 runs from her four overs without picking up a wicket.
In their reply, the Renegades batted decently but fell short of their target in the end, finishing 159-6 from their 20 overs. Matthews was good at the top of the innings with a quick 19-ball 35 including six fours while Carly Leeson ended not out on 34 against New Zealand leg-spinner Amelia Kerr’s 2-27 from four overs.
Matthews’ Renegades are currently fifth in the eight-team table with two points from as many games.
Bushfires are raging across Australia, with New South Wales and Victoria greatly affected.
The nation's sportspeople are rallying to help those impacted, with Brisbane Heat star Lynn and the Melbourne Stars' Maxwell offering their help.
"Hey guys, for every six I hit in this year's Big Bash League I will donate $250 towards the Red Cross Bushfire Appeal," Lynn wrote on Twitter on Friday.
"It is special to see so many athletes from various sports getting in behind the real heroes who are fighting to save lives and properties around our country."
Maxwell wrote: "Love it Lynny!! I'll match you on $250 per six I hit in this year's BBL.
"Great cause which is helping so many people around the country who are doing it tough right now."
Maxwell and Lynn are two of the BBL's biggest hitters and have tallied nine and 12 sixes respectively so far this season.
It comes as tennis star Nick Kyrgios vowed to donate 200 Australian dollars for every ace he hits during the summer Down Under.
Illawarra Hawks star LaMelo Ball, meanwhile, pledged to donate a month of his NBL salary to help victims.
Hosein took three wickets and scored a quick-fire 30 for Melbourne after Russell had bludgeoned them back into contention after a Michael Neser’s hat-trick had threatened to deny them victory.
Brisbane won the toss and chose to bat first but were two wickets down for 14 in the third over thanks to Mujeeb ur Rahman and Hosein who claimed the wickets of Max Bryant for five and Colin Munro for eight, respectively.
However, knocks of 25 from Sam Billings, 29 from Matt Renshaw and an unbeaten Jimmy Peirson helped stage a recovery. However, after a partnership of 61 between Billings and Renshaw both were dismissed by Tom Rogers in the 11th over as Brisbane slipped to 78-4.
It was soon 96-5 as Rogers dismissed Ross Whitely for 8 in the 15 over.
Hosein took the wickets of Neser (3) and James Bazley (0) in three balls in the 15th over. Peirson smashed 45 from 30 balls with six fours to get Brisbane to a competitive 138-7.
Rogers ended with 4-23 while Hosein took 3-26 in another solid performance with the ball.
Melbourne’s relatively simple chase of just under seven runs an over, became extremely difficult when Neser ripped through the top order with just nine runs on the board.
He dismissed Sam Harper first ball and then Jake Fraser-McGurk from the final ball of the first over and then in his second dismissed Nic Maddinson for two and Johnathan Wells for a duck in consecutive balls of his second over to leave Melbourne facing defeat.
However, Russell and Aaron Finch staged a recovery would set the team firmly on the path to victory.
Russell hit two fours and six sixes and he and Finch put on 81 for the fifth wicket before he got out caught behind off Mark Steketee for 57 from 42 balls.
Hosein picked up from where Russell left off hitting two fours and two sixes in a 39-run partnership with Finch. He eventually holed out to deep midwicket for 30 from 19 balls off the fifth ball of Steketee’s final over with Melbourne needing just nine from seven balls.
Will Sutherland smashed Steketee’s last ball for a massive six over the midwicket boundary leaving Finch to hit the winning runs, a four over extra cover to seal with victory from Bazley’s second ball of the final over.
Melbourne’s third straight win means they have six points and only trail leaders Adelaide Strikers on net run rate.
The Heat were stunningly bowled out for 100 in their innings at The Adelaide Oval, Matt Renshaw (43) and captain Chris Lynn (26) the only players to reach double figures.
Adelaide reached the modest target of 101 with 9.1 overs to spare, Salt and Jake Weatherald (33) securing their biggest BBL win ever by balls remaining.
They are third in the table with 11 points from 10 games. Brisbane are a point behind them in fifth.
BRISBANE FAIL TO HEAT UP
The visitors' innings never got going, and the Heat were two down inside the first four overs when AB de Villiers (2) was taken at deep square.
Lynn and Renshaw's stand of 35 briefly steadied the ship, but when the former went to Liam O'Connor (3-30) the Heat fell apart.
Renshaw found nothing in the way of support as a talented attack featuring Michael Neser and Rashid Khan along with Peter Siddle ripped through the Brisbane line-up.
PHIL WORTH HIS SALT
Salt has struggled for form since his half century against the Melbourne Renegades on December 29.
However, the opener proved his worth with an excellent display of ball striking.
He hit five fours and five sixes in a superb showing, with Weatherald - who found the rope six times - more than playing his part as Adelaide eased to a victory that was fittingly sealed with a Salt maximum.
All eyes were on Sixers batsman Smith in his first BBL appearance for six years, while Heat batsman Marnus Labuschagne played his first match of the 2019-20 tournament after returning from Australia's ODI series in India.
Labuschagne made only three as the Heat were restricted to 126-8, with runs hard to come by on a slow Gabba surface on Thursday.
Steve O'Keefe was named man of the match after taking 1-20 from his four overs, while Jackson Bird, Tom Curran and Ben Dwarshuis took two wickets apiece.
The Sixers eased to their target with 25 balls to spare, Vince making a stylish 51 off 37 balls and fellow opener Philippe an unbeaten 52 from 43.
Smith fell for only nine, but the Sixers were all-but home by then as they moved above Adelaide Strikers into second spot in the battle to face Melbourne Stars in the first Qualifier at the MCG.
The Heat have now lost three in a row and are just outside the play-off spots with two games to play.
STRUGGLING HEAT BATSMEN FAIL TO FIRE
O'Keefe stuck a big blow by removing Chris Lynn's off stump in the third over and the Heat were 33-2 in the fifth when Matt Renshaw was removed by Bird, having struck Nathan Lyon for six and four in the previous over.
Lyon had Sam Heazlett caught and bowled before Labuschagne was taken by Smith attempting to pull Curran, with the Heat slumping to 57-5 halfway through their innings.
James Pattinson made a brisk 27 not out from 15 balls after AB de Villiers (25) was caught by Smith in the deep, but the Sixers bowlers did a great job of restricting the Heat to a below-par total.
VINCE PROMOTION PAYS OFF
England batsman Vince was promoted to open with Philippe, Daniel Hughes dropping down the order.
He made the most of his opportunity at the top of the order, full of confidence after making an unbeaten 41 in a victory over the Melbourne Stars last time out.
Vince showed his class with glorious strokes on both sides of the wicket, coming down the track to launch Mujeeb Ur Rahman into the stands and reaching his half-century off 34 balls with a classy drive over cover before pulling Ben Laughlin to Heazlett.
PHILIPPE RETURNS TO FORM, SMITH MISSES OUT
Wicketkeeper batsman Philippe had mustered only 32 in his previous five knocks, but returned to form in batting conditions that were not straightforward.
Vince comfortably outscored Philippe in a stand of 75, but the 22-year-old clattered Laughlin for 10 off two balls as the Sixers closed in on an emphatic victory.
Pattinson followed Smith and had his Australia team-mate caught behind when he moved outside leg stump attempting an expansive drive, but Philippe brought up his half-century before Moises Henriques put the Heat out of their misery.
The weather saw a delayed start and then limited Brisbane to just eight overs in the first innings, but Banton quickly made up for lost time in a 16-run triumph.
The England international needed just 16 balls to reach 50, ending on 56 after seven sixes that helped Heat to an impressive 119-4.
Further rain appeared the only hindrance to a dominant win, and neither the conditions nor Thunder - chasing 77 in a reduced five overs - could effectively intervene.
BANTON BLOWS THUNDER AWAY
Banton started as he meant to go on when the covers came off, launching Daniel Sams over the boundary from the first ball.
And this rapid progress continued alongside fellow opener Chris Lynn, lifting Brisbane to 39 without loss by the end of the two-over powerplay.
But it was a blistering fourth over that stole the show, Banton following up a rare dot ball with five successive maximums to bring up his half-century in sensational style.
The second six in that stretch had been carried over the rope by Brendan Doggett as he desperately tried to check the 21-year-old's thrilling assault.
HEAT HALTED AS RAIN RETURNS
A partnership of 90 was finally ended in the fifth over, as Banton hit a Chris Tremain full toss to Chris Morris on the fence.
That prompted something of a collapse, with Heat only able to add another 29 runs.
Doggett held on impressively to account for Lynn (31), before Sams (2-24) removed Max Bryant and Matt Renshaw.
Thunder's hopes of victory were extremely remote and they were 18-1 after two overs, but Brisbane were dealt a blow when rain fell again with the match still 2.5 overs short of the requisite number of deliveries.
SAMS CARRIES SYDNEY'S HOPES
With Sydney then facing a tough total as play resumed, Callum Ferguson launched towards the boundary but was caught before Alex Hales (21 not out) struck consecutive fours.
An entertaining fourth over saw three boundaries and two wickets, and Thunder's chances were all but over when Sams' (10) six-four start was followed up with a stunning grab out of the air from Ben Laughlin.
They could only reach 61-4, as Ben Cutting saw out the fifth and final over with an array of yorkers.
