Australia score modest 263 against India thanks to Khawaja and Handscomb
While the total did not quite vindicate Pat Cummins' decision to bat first, it was still better than the 177 and 91 Australia managed in their two innings in Nagpur where they were hammered inside three days.
On three occasions Australia lost wickets either in the same or in successive overs, stymieing any rebuilding efforts in their stop-start innings.
India hit 21 runs off the last nine overs of the day with skipper Rohit Sharma (13) and KL Rahul (four) both not out at the close.
With all-rounder Cameron Green and paceman Mitchell Starc still recovering from finger injuries, Australia took a bold selection gamble that left Cummins as their lone fast bowler.
Travis Head replaced fellow batter Matt Renshaw, but a bigger surprise was the inclusion of Matt Kuhnemann for his test debut as Australia's third spinner at the expense of paceman Scott Boland.
"If we can negotiate the turn and bounce, it's not a big total and they have just one fast bowler in their ranks," India seamer Mohammed Shami, who claimed 4-60, told reporters.
"If we can take a decent lead, it could come in really handy."
Cummins opted to bat on a track that offered significant bounce but their openers endured a tough opening hour at the Arun Jaitley Stadium.
David Warner, who managed scores of one and 10 in their innings defeat in Nagpur, needed 21 balls to open his account.
By then he had already survived on review after being given lbw to Mohammed Shami (4-60).
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Warner struggled against Mohammed Siraj in particular and was hit twice, once on the arm and then on the helmet, before Shami dismissed him caught behind for 15.
Marnus Labuschagne (18) hit four fours before Ravichandran Ashwin (3-57) struck twice in three balls to wreck Australia's top order.
Labuschagne, rapped on the pad, was initially ruled not out but had to leave after India reviewed.
Steve Smith fell two balls later, caught behind for a duck, but Khawaja kept going.
The left-hander looked well set for his century before attempting a reverse-sweep against Ravindra Jadeja (3-68) and Rahul at point leapt to his right to pluck a spectacular one-handed catch out of the air.
Alex Carey fell in the same over before Cummins produced a belligerent cameo of 33 and Handscomb helped take Australia past the 250 mark before they wilted.
"I don't know a par score until India bats on it," Khawaja said.
"They're very good in their conditions. I think now we have three spinners in the team, especially on that wicket, it’s going to be challenging, just like their spinners were very challenging."
The home side brought in Shreyas Iyer for Suryakumar Yadav in the only change to the squad that triumphed in Nagpur.