The opener, whose place for the first Test is under threat, fell for just one in the second innings, trapped lbw by Mohammed Shami in Sydney.
Burns has been in poor form ahead of the series opener beginning in Adelaide on Thursday.
The right-hander fell for a duck in the first innings, while he made scores of four and 0 in the previous tour match.
It comes after Burns scored just 57 runs in five Sheffield Shield innings for Queensland to begin the season.
His form comes at a time when Australia are dealing with injuries to top-order batsmen, with David Warner (adductor) and Will Pucovski (concussion) already ruled out of the first Test.
Burns' combination with Warner had been talked up before the explosive left-hander suffered his injury.
In 27 Test innings, Burns and Warner have scored 1,365 runs at an average of 50.55, including averaging 65.4 against Pakistan and New Zealand in 2019-20.
Marcus Harris, who like Pucovski was in good form to begin the Shield season, made scores of 26 and five, having departed for 35 and finished with 25 not out in the first tour game.
The top-order woes have led to suggestions Shaun Marsh, 37, could return, with only Pucovski (495) having scored more Sheffield Shield runs than his 485 this season.
But frmer Australia wicketkeeper Ian Healy hopes Australia look elsewhere.
"I hope not. Not because it's Shaun, but because we've got heaps of players that have performed in those Shield games and you don't have to go back to a 37-year-old player," he told SEN.
"I want to see him play Shield cricket for as long as he wants and help a lot of blokes, but we're better than having to go back to Shaun I reckon."
Khawaja, 33, was dropped from the Test team during last year's Ashes, while his last ODI was also in 2019.
Marsh, 36, has been out of international action since mid-2019 and was also left off a 20-player list named on Thursday.
"As Mitch Marsh and Matthew Wade have proven there are always plenty of opportunities for those who have missed out to be reselected by performing consistently at domestic level; and importantly to make the most of any opportunity that comes their way at international level," Australia national selector Trevor Hohns said in a statement.
"As is always the case there are unlucky omissions but, however, because you are not on the list does not mean you cannot be selected to represent Australia."
Marnus Labuschagne, Joe Burns, Matthew Wade, Mitchell Marsh, Kane Richardson and Ashton Agar were called up to the nationally contracted list.
It continues Labuschagne's incredible rise, with the right-hander averaging 63.43 in 14 Tests and 50.83 in seven ODIs.
"We feel all deserve their inclusion recognising the performances of those players in the past 12 months and, as importantly, what they can offer in the next 12 months," Hohns said.
"Marnus' rise has been meteoric and well documented, Joe has been a good Test match player, Ashton Agar’s form in T20 internationals has been exceptional, while Kane Richardson has been outstanding in the 20-over and one-day games.
"Matthew Wade's summer showed he is not only a tough but a good Test player for us. His form extended into white-ball cricket late in the summer, earning him well-deserved call-ups to the one-day and T20 Australian squads.
"After missing the list last year Mitch Marsh's recent form showed he has a lot of international cricket ahead of him as a batting all-rounder. Mitch proved this with his man-of-the-match performance against New Zealand at the SCG in the last game Australia played and a five-wicket haul in the last Test match he played on the Ashes tour."
Cricket Australia contracted player list: Ashton Agar, Joe Burns, Alex Carey, Pat Cummins, Aaron Finch, Josh Hazlewood, Travis Head, Marnus Labuschagne, Nathan Lyon, Mitchell Marsh, Glenn Maxwell, Tim Paine, James Pattinson, Jhye Richardson, Kane Richardson, Steve Smith, Mitchell Starc, Matthew Wade, David Warner, Adam Zampa.
An eight-wicket trouncing in front of a crowd of 54,478 on Saturday reflected the changing fortunes of these teams since they met at nearby Docklands Stadium in the title match 11 months ago.
Michael Klinger's Renegades have gone into reverse gear this season and this was a sixth straight defeat for the defending champions, who are proving to be a shadow of the side led by Andrew McDonald last season.
The Stars have soared to the top of the table with five wins in six games for David Hussey's side, who scythed down the Renegades from 117-2 to their eventual 142-9 total.
Shaun Marsh and Beau Webster looked like lifting the Renegades to a substantial total as their third-wicket partnership reached 62.
Yet Marsh's dismissal for 43 to a brilliant boundary catch, Ben Dunk tossing the ball back to Nathan Coulter-Nile, off Sandeep Lamichhane's leg spin triggered a collapse, with Dan Christian stumped for a golden duck and Webster also soon back in the dressing room.
Marcus Stoinis anchored the Stars response with an unbeaten 68 from the top of the order to becoming the leading scorer in the competition, with skipper Glenn Maxwell plundering a snappy 40 not out as the Renegades attack sorely lacked bite.
Khawaja and Marsh were among those to miss out on national contracts, with a 20-man list named by Cricket Australia (CA) on Thursday.
Marsh, 36, last played for Australia in mid-2019, having featured in 38 Tests, 73 ODIs and 15 Twenty20s for the country.
But Hohns said Marsh's time playing for Australia was probably over.
"Shaun, you never say never, and I'll never say never of course, but I think Shaun, I think he's now 36 or 37, is probably past representing Australia," he told a video conference on Thursday.
"We've spoken to Shaun regularly over the last 12 months and he understands the situation. He's been a wonderful player in domestic cricket, he's played some very, very good innings for Australia in Test match cricket and he'll be sorely missed.
"But what is good is that he's continuing to play the game and as a senior player playing domestic cricket around Australia, he's got a big role to play and as I suggested it's great to see players like that continuing to play and put back to state cricket."
As for Khawaja, Hohns said leaving out the left-hander was the toughest decision.
The 33-year-old batsman has not played for Australia since being dropped during last year's Ashes series.
"Usman is one of the unlucky ones, there's no doubt," Hohns said. "As we know, Usman didn't play cricket for Australia last year at all in any format after being dropped from the Ashes series.
"If I'm looking at Test cricket, Usman's form in domestic Shield cricket didn't demand that he was chosen for Australia and I think that's pretty fair. One-day cricket, he didn't play for Australia despite being a very good performer in the Marsh Cup early in the season, but the area that he operates in, like a couple of our unlucky omissions, is up the top and we're pretty well looked after up there with [Aaron] Finch, [David] Warner, [Steve] Smith and now Marnus Labuschagne so it was a difficult time for him and then of course in T20 cricket he hasn't played for Australia for some time.
"Usman obviously received rankings in a couple of those forms of the game, but those rankings weren't sufficient enough to get him into the contract list in the end."
