India began day two at 303 for four and proceeded to twist the knife against a demoralised home team that toiled in hot conditions with little joy.
Ravindra Jadeja chipped in with a lively 81 in a 204-run stand with Pant -- a record seventh wicket partnership at the Sydney Cricket Ground.
Skipper Virat Kohli finally declared at 622 for seven when Jadeja was out, with the tireless Nathan Lyon taking 4-178 off 57.2 gruelling overs.
It left new-look Australian openers Marcus Harris (19) and Usman Khawaja (five) to negotiate 10 tricky overs before stumps after a torturous day in the field. They ended at 24 without loss.
The visitors lead the series 2-1 after winning the opening clash in Adelaide and the third in Melbourne. Australia claimed victory in Perth.
Calm and collected number three Pujara started the day 130 not out and picked up where he left off.
He drove his second ball through the covers for three before once again dropping anchor, blocking and targeting only loose balls.
Pujara brought up his 150 with a boundary and seemed destined for his fourth Test 200 before attempting to whip Lyon down the leg side. Instead, he lobbed the ball back into the spinner’s hands.
He survived a review decision for caught behind on 12 and was dropped on 192 by Khawaja, but was otherwise faultless. AFP