Chasing a stiff target of 349 for a win, India started off well but suffered a dramatic collapse in the post tea session to just about eke out a draw by finishing on 252 for seven in 89.5 overs on an absorbing fifth day's play at the SGC.
India were comfortably placed at 160 for two at tea and needed 189 runs off 33 overs for a win in the final session.
But Ajinkya Rahane (38 not out) and Bhuvaneswar Kumar (20 not out) played out almost 12 tense overs to save the game for the Indians, who were badly let down by their wayward bowlers right through the series.
The 2-0 series verdict meant that Australia regained the Border-Gavaskar trophy by virtue of their victories in Adelaide and Brisbane. The Boxing Day Test at Melbourne ended in a draw.
The stage was set for a pulsating fifth day's play with Australia declaring their second innings at the overnight score of 251 for six, giving India a target of 349 in 90 overs to register their first win in the series.
India lost young opener Lokesh Rahul (16) early but Vijay and Rohit Sharma (39) stitched 56 runs for the second wicket to stabilise the innings.
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