Batting after captain Pat Cummins won the toss on a steamy day, they were an ominous 176-2 by the break at the Melbourne Cricket Ground.
Marnus Labuschagne was not out 44 and Steve Smith on 10 with Khawaja (57) the only wicket to fall in the second session, where 64 runs were added.
A carefree Konstas was out before lunch for a whirlwind 60 off 65 balls in a debut to remember, slamming 18 off one Jasprit Bumrah over and having a run-in with superstar Virat Kohli.
The five-match series is locked at 1-1 after India won by 295 runs in Perth before being crushed by 10 wickets in Adelaide. The rain-affected third Test in Brisbane was drawn.
Nathan McSweeney was axed after failing to fire in the first three Tests but Konstas and Khawaja shared in an 89-run opening partnership -- the hosts' best of the series -- before the 19-year-old was undone by the spin of Ravindra Jadeja.
Called up in place of McSweeney, Australia's youngest-ever opener opted to face the first over from a menacing Bumrah and survived despite the Indian spearhead repeatedly beating his bat.
But Konstas kept his focus and scored his first Test runs in Bumrah's next over with a gentle flick through backward square leg.
He said before the match he had a plan to combat Bumrah and, as he got his eye in, he incredibly reverse ramped him for two fours and a six in one over, bringing the crowd alive.
A frustrated Kohli forcefully bumped shoulders with him at one point and they exchanged words, which could get both players in trouble if the match referee takes the matter further.
But the teenager was unphased by the run-in and slammed 18 off the next Bumrah over, including another six.
His half-century came off just 52 balls with two from Mohammed Siraj -- the third-fastest on debut for Australia.
At the other end Khawaja, twice the age of his opening partner, was content to be the support act, grinding his way to a 27th Test 50 in a welcome return to form.
Bumrah finally removed him after a 121-ball stay with Khawaja's pull shot going only as far as KL Rahul at midwicket, leaving Labuschagne and Smith to see them to tea.
Australia made two changes for the match, with seamer Scott Boland also in for the injured Josh Hazlewood, while India dropped number three batsman Shubman Gill in favour of Washington Sundar as a second spin option.
