Nightwatchman Nathan Lyon was the unlikely top scorer for Australia, falling on 41 with his first Test 50 in sight.
Cameron Green continued his form with 34, but all-rounder Phillips spun his way to five wickets and was on a hat-trick after removing Travis Head for 29 and dismissing Mitch Marsh with the next ball.
Phillips finished with 5-45 as Australia were all out for 164.
The Australians struck early in the Blackcaps innings, Lyon dismissing Tom Latham and Kane Williamson for single-digit scores, before part-timer Head removed Will Young for 15.
Rachin Ravindra (56 not out) and Daryl Mitchell (12 not out) dug in for the rest of the day.
Two days remain with New Zealand requiring 257 pull off what would be an incredible victory.
Green underwent surgery after breaking his right index finger during a victory over South Africa in the Boxing Day Test at the MCG.
Starc damaged his middle finger in the same match in Melbourne, with both players missing out as Australia attempt to secure a 3-0 whitewash of the Proteas at the SCG.
Australia start the first Test against India in Nagpur on February 9 and Green believes that contest could come too soon for himself and paceman Starc.
He told SEN WA: "I think me and Starcy are maybe touch and go for that first one but obviously we'll give ourselves the best chance.
"[It's] going well. Had successful surgery in Sydney and the surgeon is really happy with how it went. I think he did Tim Paine's successful surgery, so it fills me with a lot of confidence.
"The rehab is having two weeks of time [off], then two weeks to start running and get the shoulder and back moving just to double-check they haven't frozen over. Then probably at the four-week mark I'll try and hold a ball and see how that works.
"Try and hold a cricket bat and see how it feels. At the moment [the finger] feels really good, pain-free, so that gives me a bit of confidence in four weeks' time that it will be all good.
"We meet over in Sydney for the Allan Border Medal [ceremony], then we leave the next day to go to India."
Starc also dismissed talk that he may not be able to bowl for the Mumbai Indians at the start of his first Indian Premier League campaign.
He said: "No, that's not correct. I've heard about this for quite a while now. I don't know where it's come from. We've spoken to the selectors. I've heard that I'm 100 per cent available for both skill sets in the IPL at the start, so I'm not too sure where that's come from.
"Obviously my first priority is the Test series that's beforehand, getting myself right for the first Test."
The Australians, who lead the three-game series 1-0, are 45-1 in reply with David Warner, playing his 100th Test, surviving through to stumps on 32 not out alongside Marnus Labuschagne (5no).
Australia captain Pat Cummins raised a few eyebrows by opting to bowl after winning the toss but will feel justified given the state of play, while South Africa have now gone seven Test innings without reaching 200.
The Proteas slumped to 67-5 with local hero Scott Boland claiming the opening wicket of Sarel Erwee (18) before some brilliance from Labuschagne in the field, running out skipper Dean Elgar for 26 with a direct hit before pulling off a flying catch to dismiss Khaya Zondo (5).
But Kyle Verreynne and Marco Jansen led the rearguard, which had the hosts worried before Green took centre stage with his ability to swing the old ball.
He dismissed both Verreynne (52) and Jansen (59) with edges to first slip Steve Smith and wicketkeeper Alex Carey respectively.
Verreynne and Jansen had combined for a 108-run stand which was only South Africa's third 100-run partnership of the calendar year.
From there, Western Australian all-rounder Green made light work of the tail to finish with 5-27 as the Proteas' final five wickets fell for just 10 runs.
In 12 overs late in the day, Australia lost Usman Khawaja (1) who was caught behind by Verreynne off Kagiso Rabada, while under-fire Warner appeared focused in his milestone game and navigated his way through to stumps.
Starc injury concern for Aussies
Green's five-wicket haul came at a good time for Australia with Verreynne and Jansen appearing settled, but also with left-arm quick Mitchell Starc nursing a finger injury.
Starc spent time off the field for treatment on the middle finger of his bowling hand after diving to catch Jansen's lofted shot to long-on, returning with heavy taping on the issue.
Local hero delights again
Boland only finished with 1-34 from his 14 overs but the Victorian right-arm fast bowler was cheered by his parochial crowd throughout, dating back to his heroics at the same venue 12 months ago in the Ashes when he took 6-7.
Boland got the opening wicket with perfect line and length, drawing an edge from opener Erwee to third slip Khawaja.
The all-rounder became the most expensive Australian player in competition history when he was sold for 17.5 crore (£1.75million) to Mumbai Indians, trailing only England's Sam Curran (18.5 crore, £1.85m) overall.
Green followed up his giant fee with a blockbuster red-ball performance to reinforce his credentials on Monday as well, with a five-for on the first day of the second Test against South Africa at the MCG.
But Green acknowledged he was yet to feel as if he had lived up to his price-tag, while thanking his team-mates for ensuring his feet stay earthbound.
"To be fair, I think I didn't do much to kind of earn that," he said. "I just put my name into the auction, and it just happened.
"It doesn't change who I am or how I think and all the confidence I have in my cricket. Hopefully, I didn't change too much.
"The players [here] can bring you back down pretty quickly. It's a good group that we've got at the moment. Everyone gets around you when they need to and can bring you back pretty quickly when they want to.
"I think everyone was focused on Boxing Day. It's a fixture that you point out at the start of the year, and you look forward to, so now that takes your focus 100 per cent."
Green's effort with the ball could be essential for Australia going forward, after Mitchell Starc suffered a finger injury while fielding on day one.
The fast bowler faces a wait to discover if he will be able to take part in the rest of the Test match against the Proteas.
Green was not included when Australia picked their 15-man group five weeks ago.
The impressive form of the 23-year-old since that selection has caught the eye, with two half-centuries in three innings against India last month showcasing his attacking talent.
Yet Finch sees his squad as being settled, with Mitchell Marsh and Marcus Stoinis on the way back to full fitness after respective ankle and side strain injuries.
Asked about Green's prospects of playing in the tournament, Finch said: "I'm not sure at the moment – I don't think so."
This is not to say Finch cannot see Green contributing immensely to Australia in the short and long term, but the World Cup decision has been taken.
"It's just one of those things," said Finch. "He had a really good tour of India, it was good for him to get an opportunity to open the batting, so he'll get more opportunities.
"He'll get an opportunity at some point in this series. The reason we've carried him is to have an extra bowling resource as well.
"Obviously his batting is exceptional, and he shows a lot with the ball. He keeps developing and he keeps improving every time he gets an opportunity."
David Warner and Mitchell Starc have returned to the Australia ranks after missing the short India series.
Australia have won two of their last three men's T20Is against West Indies (L1), including an eight-wicket victory in their most recent meeting last November.
Wednesday's series opener in Carrara will be the fourth men's T20I between the teams in Australia, and the first since West Indies won the last such game in February 2013, having been beaten in their previous two against the hosts.
Finch, Hazlewood, Cottrell closing on landmarks
There is a landmark for Finch to chase, since he is 85 away from becoming the sixth player to score 3,000 runs in men's T20I history and the first from Australia.
The skipper has struggled against the Windies, however, averaging 19.5 in eight previous T20I innings, with a high score of 53 against the Caribbean side.
West Indies have been pushed into a World Cup squad change after batter Shimron Hetmyer failed to make his intended flight, with Shamarh Brooks promoted to take his place.
Brooks is not yet in Australia, where the coming games will see a pace bowler from each side look to reach 50 wickets in T20I matches.
Australia's Josh Hazlewood is on 49, putting him one away from becoming the third Australian man to reach 50 wickets in the short format, after Adam Zampa and Mitchell Starc.
Wednesday's game will be Hazlewood's 34th T20I, and only three quicks have reached 50 wickets in fewer matches: Mark Adair, in 28 matches for Ireland; and Mustafizur Rahman, who reached the mark in 33 games for Bangladesh.
West Indies' Sheldon Cottrell has 48 wickets in the format to date, two short of becoming the fourth men's West Indies bowler to take 50, following Dwayne Bravo, Samuel Badree and Sunil Narine.
Kohli smashed seven fours and six sixes in his 47 balls faced as the Challengers set the Kings a daunting target of 241, with Rajat Patidar also bringing up his half-century and Cameron Green (46 off 27) falling just short of doing so.
The Kings pulled off the biggest run chase in IPL history less than two weeks ago, but their hopes of another comeback were dealt a huge blow when Faf du Plessis took a wonderful over-the-shoulder catch to send Jonny Bairstow packing with Punjab at 71-1.
Kohli's contribution wasn't only limited to the bat, as he produced a stunning run out of Shashank Singh, haring onto the scene to send wickets flying with an underarm throw as Shashank failed to make it back by mere inches.
It was then up to Mohammed Siraj to polish off the Punjab tail, finishing with figures of 3-43 as the Kings fell to back-to-back defeats, keeping them ninth in the standings.
Data Debrief: Kohli leads the way
Having previously claimed the honour in 2016, Kohli leads the way in the race for the 2024 Orange Cap, another impressive innings taking him to 634 runs for the campaign.
Averaging 70.44 with a strike rate of 153.51, Kohli put further distance between himself and Chennai Super Kings' Ruturaj Gaikwad, whose 541 runs put him second in the standings.
A comfortable 35-run away win over Sunrisers Hyderabad on Thursday has lifted spirits for RCB after they had fallen just one run short of reaching a big Kolkata Knight Riders total in their previous outing.
RCB remain bottom of the standings going into back-to-back matches against the Gujarat Titans, but they approach that double-header with new-found confidence after snapping a miserable six-match losing streak.
"In the last two games we have shown great signs of fight," Du Plessis said.
"The [first] SRH game we got to 260 [pursuing a big target], then the KKR game as well, just one run [short]. It was almost a record chase.
"We have been close for a while, but you need to win matches to get confidence back in the group.
"It is a massive relief. No matter where we are, when you are not winning it does affect you, it does affect you mentally, it does affect your confidence.
"I will sleep a bit easier. For the first half of the tournament only it was only Virat contributing. It is important as a batting line-up to contribute together because we have seen the scores are so big, it's never going to be just one guy scoring the runs."
Kohli still impressed against SRH, with his 51 – along with a rapid 50 off 20 balls from Rajat Patidar – helping RCB to score 206-7 after opting to bat first.
There was also a strong outing from Australia all-rounder Cameron Green, who scored 37 not out before taking 2-12 from two overs with the ball and grabbing a huge catch to dismiss SRH dangerman Heinrich Klaasen for just seven.
Du Plessis added: "The last week and a half we have been working hard to make sure we get better at our own game.
"You can see the last game; there is some confidence in our batting. We have got more guys scoring runs now. Rajat playing two really good innings back-to-back, Greeny getting runs. It is massive for him just to get that load off his shoulders.
"You can't speak confidence into the group, you can't fake confidence into the group. The only thing that gives confidence is performance.
"First half of the competition we certainly felt like we weren't near our full potential. And when you're playing at 50% or 60%, obviously, you try 100%, but you don't get the confidence in your group.
"The competition is so strong, the teams are so strong that you'll get hurt [if you are not at 100%]."
Green thought Du Plessis had taken a risk by choosing to bat first, but it was a decision that paid off.
He said: "It was [a brave call]. I definitely wasn't in agreement with [batting first] so credit to the captain and coach. SRH have been batting beautifully when they bat first - that was the main reason.
"We always have to celebrate little wins and we feel pretty good now. Always nice to be back to winning ways."
Asked about his catch to dismiss Klaasen, he added: "I think the whole time I kept thinking 'Klaasen, Klaasen' in my head!
"It was up there for a while, happy I hung on to it."
RCB are away to the Titans on Sunday, before playing at home against Shubman Gill's side on May 4.
Resuming day two on 255-4, Khawaja (180) and Green (114) piled more runs on to frustrate the hosts with a fifth-wicket partnership of 208, while Australia's tail also wagged.
Ravichandran Ashwin produced figures of 6-91 to stop the tourists from doing even more damage, before Rohit Sharma (17 not out) and Shubman Gill (18 not out) made a promising start to India's reply, ending the day 36-0, still trailing by 444 runs.
Khawaja and Green continued their impressive partnership from day one, with the latter hitting his maiden Test century before a sweep attempt saw him glove one from Ashwin to Srikar Bharat.
Ashwin soon found his groove as he removed Alex Carey for a duck and Mitchell Starc for six, while Khawaja was finally out lbw after a review off the first ball after the tea interval from Axar Patel.
Lyon (34) and Murphy (41) were in the mood to play some shots though, and had plenty of joy as they struck 11 fours between them in a ninth-wicket partnership of 70, before both fell to Ashwin.
The surface in Ahmedabad has been kinder to batters than others in the series, and Rohit and Gill had few problems seeing off Australia's bowling attack in their 10 overs before close.
Gill launched the first six of the match in the final over of the day off Lyon, but India still have plenty to do to get close to the Baggy Green's first innings total.
Khawaja shows patience is a virtue
Khawaja had already reached three figures on day one, but continued his impressively mature innings alongside Green on Friday, lasting 422 balls in all, the most faced of any Australian batter in an innings in India in Test history.
After the day ended, Green said: "Ussie helped me so much out there. It is really special."
Ashwin overtakes Kumble in Australia battles
It must be a strange feeling for a bowler to post numbers as impressive as 6-91 but see the opponents still score almost 500 runs.
It may be consolation for Ashwin that his 113 wickets in total means he has surpassed Anil Kumble (111 wickets) and equalled Lyon to become the joint-leading wicket-taker in the Border Gavaskar Trophy.
Meanwhile, Jason Holder went to Rajasthan Royals and Odean Smith went to Gujarat Titans.
Chennai Super Kings, Mumbai Indians, Lucknow Super Giants and Rajasthan Royals all got involved in the bidding for Curran, forcing the price up, before Punjab won out.
Curran was outstanding in the T20 World Cup, taking 13 wickets – including 3-12 against Pakistan in the final last month.
There was a clamour for top-tier all-rounders, with Mumbai Indians landing Australia's Cameroon Green for 17.5 crore (£1.75million),
England Test captain Ben Stokes was wanted by Sunrisers Hyderabad and Lucknow, but it was Chennai who got him for 16.25 crore (£1.65million).
That fee for Stokes matched the previous record for an IPL player, set when Rajasthan signed Chris Morris ahead of the 2021 competition.
New Zealand white-ball skipper Kane Williamson had been the first player available in the auction and went for a bargain 2 crore (£200,000), before a bidding war broke out for England's Harry Brook.
Rajasthan were edged out as he went to Sunrisers for 13.25 crore (£1.325million), the highest price ever paid in an Indian Premier League auction for a specialist batter before Pooran went under the hammer.
Cameron Green (79) and Alex Carey (67) frustrated Pakistan in the heat on Tuesday before Naseem Shah (4-58) and Shaheen Shah Afridi (4-79) prevented the tourists from going beyond 400 in Lahore.
Pat Cummins dismissed Imam-ul-Haq cheaply, but an unbroken stand of 70 between Shafique (45 not out) and Azhar Ali (30no) took Pakistan on to 90-1 at the close - trailing by 301 runs.
Carey and Green took Australia from 232-5 at the start of play to 320-5 at lunch, bringing up their half-centuries as the Pakistan attack toiled.
Nauman Ali ended a sixth-wicket stand of 135 by trapping Carey bang in front and Naseem cleaned Green up with an excellent delivery.
Australia lost five wickets for 50 runs, with Afridi removing Mitchell Starc and making a mess of Mitchell Swepson's stumps after the impressive Naseem bowled Nathan Lyon.
Imam (11) was snared lbw by Cummins off balance in the 12th over of Pakistan's reply to end an opening stand of 20, while Shafique was fortunate to edge between Carey and Steve Smith in the slips.
Azhar clattered Lyon down the ground for six and Shafique ticked along nicely in great batting conditions.
Cummins wasted a review for an lbw shout against Azhar as Pakistan put a frustrating start to the day behind them.
Pakistan's young pace duo fire after Carey and Green stand
Green and Carey gave Australia just the start they were looking for, but Pakistan's young pacemen fired in the afternoon session.
Teenager Naseem and 21-year-old Afridi bowled with a combination of pace and reverse swing as they cleaned up the tail in quick time.
Naseem was not selected for the second Test but he will surely be a mainstay for years to come, while Afridi has already proven he is a class act time and again.
Rock-solid Shafique
The composed Shafique has been a revelation for Pakistan at the top of the order and the opener laid solid foundations once again.
Having made a 134 and 44 in the opening match of the series in Rawalpindi before falling four short of a century in the first innings in Karachi, Shafique will be eyeing three figures again.
Smith batted as low as number nine on Test debut and has taken every spot up to number three in the course of a prolific career. Now he will head the innings for the first time having publicly pitched to replace Warner.
The 34-year-old’s move will accommodate the return of all-rounder Cameron Green in the top six for the forthcoming series against the West Indies, with Matt Renshaw picked as reserve batter and Cameron Bancroft’s hopes of returning to the Baggy Green fold dashed.
Head selector Andrew McDonald indicated all parties view the switch as a long-term move and praised the former captain for embracing change after 105 Tests and almost 10,000 runs lower down the order.
“It’s selfless that someone who’s had such success in one position or a couple of positions in the middle order, that he’s willing and hungry to have a crack at something different,” McDonald told reporters.
“For someone who has achieved as much as he has over such a long period of time across all formats, it’s a challenge or an itch he’d like to scratch and ultimately for us, as a team, it’s something that fits.
“It provides an opportunity to slot Greeny into number four where he’s had success for Western Australia. Ultimately we are trying to pick our six best batters.
“The regard in which we hold Cameron and the way the rest of that batting order is functioning left us feeling we have someone we think is pretty talented who was potentially going to find it pretty hard to get any Test cricket in the next 12 months or so.”
Inglis was ruled out of the tournament on home soil after suffering a freak injury on the golf course on Wednesday.
The wicketkeeper-batter required stitches in his right hand after the handle of his six-iron club snapped on impact during a round at the New South Wales Golf Club.
All-rounder Green was drafted into the squad two days before the holders start the defence of their title against New Zealand at the SCG.
The selection of Green leaves the hosts without a back-up keeper for Matthew Wade.
Australia head coach Andrew McDonald said: "If you look back over World Cup selections there's been plenty of times where Australia have gone in with only one frontline keeper in the squad.
"That's just to give greater flexibility to batting and bowling structures within the team. It's a conversation about how we want to give ourselves the most amount of options as opposed to covering the small risk that is there."
Australia T20 World Cup squad: Ashton Agar, Pat Cummins, Tim David, Aaron Finch (captain), Josh Hazlewood, Cameron Green, Mitchell Marsh, Glenn Maxwell, Kane Richardson, Steve Smith, Mitchell Starc, Marcus Stoinis, Matthew Wade, David Warner, Adam Zampa.
