The day started in disappointing fashion for India as Saturday's man of the moment Shikhar Dhawan (187) fell in the second over of the day and Cheteshwar Pujara followed soon after.
But Vijay (142no) steadied the ship by adding 92 for the third wicket with Sachin Tendulkar (37), who fell to Steve Smith in the over before lunch with India 24 runs behind.
After the pyrotechnics of the previous day, when he scored the quickest century ever by a Test debutant, Dhawan's departure was surprisingly low-key.
The 27-year-old pushed forward in defence to Nathan Lyon and succeeded only in prodding the ball straight into the hands of Ed Cowan at silly point, having added just one to his overnight score.
Three overs later Pujara followed when he was adjudged lbw to Peter Siddle by umpire Aleem Dar, though replays clearly showed an inside edge.
Vijay, though, was unruffled and fours in successive overs from Siddle and Lyon took him to three figures.
Tendulkar settled in at the other end, hoiking Lyon for four and elegantly driving Mitchell Starc to the boundary.
Vijay carted Xavier Doherty for six and when Tendulkar threaded the needle to drive Moises Henriques for four between cover and mid-off, he looked to be at his absolute best.
It was, therefore, something of a surprise when he edged Smith's first ball of the day to short leg, but it did not change the fact India remained in control.