Sachin challenged Aussies for more than four hours to reach his hundred and guide the tourists to 424 for seven at tea on day three, just 39 behind Australia's first innings total of 463.
Sachin reached the break unbeaten on 106 with Harbhajan not out 41 and India are in a strong position to ruin Australia's bid for a record-equalling 16th straight Test win.
Australia sniffed a chance of gaining a sizeable lead when Brett Lee bagged two quick wickets immediately after the lunch break, but Tendulkar then took over.
Wicketkeeper MS Dhoni and skipper Anil Kumble both departed for two, caught by Adam Gilchrist, who joined Mark Boucher as the only wicketkeepers to take 400 Test dismissals, off the bowling of Lee.
However, Tendulkar and Harbhajan steadied the innings with an unbroken partnership of 79, with Tendulkar drive Stuart Clark through the covers to reach his hundred off 160 balls, raising his arms in triumph. (Editing by John O'Brien)