The tourists, facing a stiff victory target of 348, collapsed from their overnight score of 31 for 3 to 168 all out 45 minutes before tea on the final day.
The leg-spinner Anil Kumble wrecked Australia's second innings with 4 for 51 to finish with eight wickets in the match. The left-arm spinner Venkatapathy Raju chipped in with 3 for 26 while the off-spinner Rajesh Chauhan made his mark with 2 for 66.
India's 17th win in their last 26 home Tests was, however, marred by four controversial umpiring decisions in the morning session which ended Australia's resistance. Three of the dubious decisions were made by the English umpire George Sharp to leave Australia tottering at 96 for 7 at lunch.
It was the Indian umpire Srinivas Venkataraghvan, however, who began the slide when he ruled Mark Waugh caught at short leg off Kumble when television replays indicated the ball may have gone off the pads. The usually unruffled Waugh, who scored 18, stood his ground for a while before walking off with Australia 54 for 4.
Then the nightwatchman Paul Reiffel was given out caught at gully by Sharp when replays showed the ball hit his front boot. It soon became 91 for 6 when Sharp ruled Ricky Ponting leg before to Venkatapathy Raju for two despite replays indicating the ball clearly pitched outside the leg stump.
Australia suffered their worst blow off the last delivery before lunch when Steve Waugh fell to another dubious decision by Sharp on 27. He played forward to Venkatapathy Raju and the ball again appeared to go off the boot to Rahul Dravid at short leg, who won his appeal for a catch.
Ian Healy, the top scorer with 90 in the first innings, delayed the end with another defiant knock of 32 not out. Healy put on 57 for the eighth wicket with Shane Warne, who made 35, before Chauhan set Australia back again with two wickets off successive balls, with Warne caught by Kumble and then Gavin Robertson bowled first ball.
Final day; India won toss
INDIA - First Innings 257.
AUSTRALIA - First Innings 328.
INDIA - Second Innings 418 for 4 dec (S R Tendulkar 155, M Azharuddin 64, N S Sidhu 64).
AUSTRALIA - Second Innings
(Overnight: 31 for 3)
P R Reiffel c Azharuddin b Ventat Raju 8
M E Waugh c Dravid b Kumble 18
S R Waugh c Dravid b Venkat Raju 27
R T Ponting lbw b Venkat Raju 2
I A Healy not out 32
S K Warne c Kumble b Chauhan 35
G Robertson b Chauhan 0
M S Kasprowicz c Srinath b Kumble 4
Extras (b4, lb3, nb4) 11
Fall (cont): 4-54, 5-79, 6-91, 7-96, 8-153, 9-153, 10-168.
Bowling: Srinath 6-4-9-1; Singh 2-0-9-0; Chauhan 22-7-66-2 (nb4); Kumble 22.5-7-46-4; Venkatapathy Raju 15-4-31-3.
Umpires: S Venkataraghavan and G Sharp.Reuse content