Batting after captain Pat Cummins won the toss on a steamy day, the hosts reached 311-6 by the close in front of more than 87,000 fans at the Melbourne Cricket Ground.
They were aided by some inconsistent early bowling and a flying start from Konstas.
The 19-year-old blasted a hugely entertaining 60 off 65 balls in a debut to remember, pounding 18 off one Jasprit Bumrah over and having a run-in with superstar Virat Kohli.
At the close, Steve Smith was not out 68 and Pat Cummins was eight. Marnus Labuschagne made 72 and Usman Khawaja 57.
All the bowlers were punished but they rallied with four wickets in the final session, including dangerman Travis Head for a duck, to haul themselves back into the contest.
Bumrah led the charge, ending with 3-75.
"It was quite surreal with the big crowd, the biggest crowd I've ever played before," said Konstas.
"I just played with freedom and backed myself. Lucky to get a few runs. A bit disappointed with the way I got out but hopefully we have got a bit of momentum for tomorrow."
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.
"A lot of credit to the way Sam played. The intent he showed sort of put us on the back foot," said Indian batting coach Abhishek Nayar.
"But it took a lot of character for our bowlers to stick in there. It wasn't the easiest conditions to bowl. At times like that it is important to stick to your plans and post-lunch we came back really strong."
With Konstas in for the axed Nathan McSweeney, he and Khawaja shared an 89-run opening partnership -- the hosts' best of the series -- before the teenager was undone by the spin of Ravindra Jadeja.
Australia's youngest-ever opener faced the first over from a menacing Bumrah and survived despite the Indian spearhead repeatedly beating his bat.
Tension
Konstas 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 see both players in trouble if the match referee takes the matter further.
"I was just doing my gloves and I think he accidentally bumped me. But that's just cricket, the tension," said Konstas.
He was unfazed and slammed 18 off the next Bumrah over, including another six.
His half-century came off just 52 balls -- 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.
Smith survived three lbw appeals from Akash Deep when they returned before India finally earned a reward when spinner Washington Sundar, in the side for Shubman Gill, tempted Labuschagne into a drive that was collected by Kohli.
The dangerous Head marched to the crease after plundering centuries in both Adelaide and Brisbane but only lasted seven balls.
Bumrah did the damage, with the Australian leaving a delivery that clattered into his off stump, before the Indian star accounted for Mitchell Marsh (4) and Alex Carey (31) fell to Deep.
Smith kept plugging away to reach a 42nd Test 50 as he targets a second century of the series.
