Chasing 216 to win, the home team eventually reached their target after a period of high drama.
It was India's second successive win at the PCA stadium. However, while the victory two years back was a comprehensive one -- by 320 runs, this was a nail-biting finish.
It was skipper MS Dhoni's [ Images ] 11th Test victory as captain in 17 matches.
Defying an injured back, Laxman proved yet again why his second innings average is close to 50, scoring what proved to be a match-winning 73 not out.
His 79-ball knock was inclusive of eight hits to the fence. In the process, he registered his 46th Test fifty, his 11th against Australia.
The Hyderabad batsman also has scored six centuries against the team from Down Under, as also his Test best -- that famous 281 at Kolkata [ Images ] in 2001.
Laxman and Ishant (31) put on a vital 81-run partnership for the ninth wicket that helped India recover from a precarious position following a batting collapse on the fifth morning.
And with the crowd cheering every run that they scored, there confidence also increased, particularly Ishant's.
However, a wrong decision on part of umpire Ian Gould cost Ishant his wicket. But a favourable decision helped Ojha (five not out) save his wicket.
And that helped India clinch the match.
It was the biggest fourth-innings target successfully chased at the PCA stadium, surpassing the 144, which India chased for the loss of one wicket against England [ Images ] in 2006.
It was also the third occasion where India beat Australia when they had to score in excess of 200 in the fourth essay.
While the only instance of such a feat happening on Indian soil came 46 years ago, when Dilip Sardesai and Mansur Ali Khan Pataudi helped the team inch past a 254-run target.
The win also preserved India's recent impressive fourth innings record. The last occasion India lost after a fourth-innings run-chase was at Sydney [ Images ] in January 2008.
Morning session: (107 runs, 25 overs, 4 wickets)
India began the fifth and final day on the backfoot. The average score batting last at the ground was 187, and the hosts needed 29 more than that.
Chasing 216 to win, the visitors had made 55 for four (after 17 overs) at stumps on day four.
Despite his injury, Laxman began on a confident note, hitting successive bounadries off Hauritz.
Tendulkar, meanwhile, completed 1,000 runs in 2010 -- the sixth time in his career that the Master Blaster had aggregated more than 1, 000 Test runs in a calendar year.
The duo put on 43 runs for the sixth wicket, in just 37 balls.
Then Doug Bollinger struck.
A short delivery forced Tendulkar to change his mind, and attempt an upper cut and Michael Hussey [ Images ] made no mistake at gully.
The veteran's 64-ball 38 was inclusive of five boundaries.
Captain MS Dhoni (2) didn't last long, finding himself short of the crease following a throw from Hilfenhaus. And India was staring at an ignomious defeat.
Dhoni's unimpressive run in the fourth innings continued. The Indian captain has scored only one half-century in nine fourth innings - against England at Lord's in 2007.
Self-proclaimed batsman Harbhajan Singh [ Images ] (2) put in another impressive effort, following his golden duck in the first innings, hitting a Bollinger delivery straight to Ponting.
Three quick wickets increased Australia's chances of a win.
After 42 overs (at lunch), the home team made 162 for eight, needing 54 runs to win.