At lunch on the fourth and penultimate day, India were 384 for three, 24 runs behind Australia's 408 all out. Vijay was batting on 142 while Sachin Tendulkar got out for 37 -- caught by Ed Cowan at forward short-leg off Steven Smith -- in what should have been the last over before lunch.
Resuming on 283 for no loss, Dhawan (187) and Cheteshwar Pujara were the two other batsmen to have been dismissed, besides Tendulkar.
The 27-year-old Dhawan, after his blistering record-breaking feat yesterday, was sent back after he could add just two runs to his overnight score of 185. He spent 251 minutes at the crease, faced 174 balls and smashed 33 fours besides hitting two sixes.
The left-handed batsman from Delhi has already broken quite a few records en route to his turbo-charged innings and was in line to rewrite a few more, before off-spinner Nathan Lyon had him caught by Ed Cowan at silly point in only the day's second over.
Vijay, meanwhile got to his century with a lofted shot over midwicket off Lyon, his patient knock a stark contrast to the one played by his opening partner.
To get to his hundred, which also is his third against Australia, the 28-year-old Chennai batsman faced 206 balls and spent 276 minutes. He struck 12 boundaries and two sixes.