Set 199 runs to win from a minimum of 23 overs, India were 73 for two when the match was called off seven overs early with Rahul Dravid unbeaten on 43 and Vangipurappu Laxman on 24.
India had resumed the final day on 362 for six, a first-innings lead of 39, and increased that to 86 before being dismissed for 409 before lunch.
The match seemed destined for a draw after more than 185 overs were lost to rain over the first three days but the home team injected some late interest with a rapid second innings.
They scored 284 for three from 62 overs to set up a declaration after tea and give themselves the faintest chance of victory. More realistically, it was also an opportunity to score psychological points before the second Test.
There was a sustained display of power hitting from their top order with Waugh (56 not out), Damien Martyn (66 not out), Matthew Hayden (99) and Ricky Ponting (50) all making half-centuries.
Hayden fell agonisingly short of his 17th Test century when he was caught on the boundary after becoming the first player to chalk up 1,000 runs in three consecutive years.
The world record holder for the highest Test innings passed 50 off 61 balls and seemed certain to get a hundred when he smashed quick bowler Ashish Nehra over his head for six to reach 99.
But, after 128 minutes and 98 balls, he swept spinner Harbhajan Singh straight down the throat of Virender Sehwag on the square leg boundary.
Ponting also threw his wicket away chasing quick runs after he completed his second 50 of the match while Waugh and Martyn, shared an unbroken stand of 128.
India suffered an early scare when openers Akash Chopra and Sehwag were dismissed by Nathan Bracken in the second over but Dravid and Laxman safely held on.
Sehwag departed for a golden duck when he skied a catch to Damien Martyn, then Chopra went next ball when he fended a delivery to Justin Langer at third slip.
Sachin Tendulkar did not come in at four because he had been off the field when his team was bowling but Dravid and Laxman had few problems, sharing an unbroken partnership of 69 in 66 minutes.
India’s first innings was soon wrapped up in the morning as fast bowler Andy Bichel had Ajit Agarkar caught at slip, then held a spectacular outfield catch in the next over to get rid of wicket-keeper Parthiv Patel without addition to his overnight 37.
Harbhajan and Zaheer Khan added a quick 41 for the ninth wicket before leg-spinner Stuart MacGill mopped up the tail.
The second Test in the four-match series starts in Adelaide on Friday.
Scoreboard
AUSTRALIA (1st Innings) 323 (J.L. Langer 121, R.T. Ponting 54; Zaheer Khan 5-95).
INDIA (1st Innings, overnight 362-6):
A. Chopra c Hayden b Gillespie 36
V. Sehwag c Hayden b Bracken 45
R.S. Dravid c Hayden b Gillespie 1
S.R. Tendulkar lbw b Gillespie 0
S.C. Ganguly c Gillespie b MacGill 144
V.V.S. Laxman c Katich b MacGill 75
P.A. Patel c Bichel b Gillespie 37
A.B. Agarkar c Hayden b Bichel 12
Harbhajan Singh not out 19
Zaheer Khan b MacGill 27
A. Nehra lbw b MacGill 0
EXTRAS (LB-6, W-1, NB-6) 13
TOTAL (all out, 120.1 overs) 409
FALL OF WKTS: 1-61, 2-62, 3-62, 4-127, 5-273, 6-329, 7-362, 8-362, 9-403.
BOWLING: Gillespie 31-12-65-4 (2nb); Bracken 26-5-90-1 (1w); Bichel 28-6-130-1 (3nb); MacGill 26.1-4-86-4 (1nb); Waugh 7-3-16-0; Katich 2-0-16-0.
AUSTRALIA (2nd Innings):
M.L. Hayden c Sehwag b Harbhajan 99
J.L. Langer c Patel b Agarkar 0
R.T. Ponting c Sehwag b Nehra 50
D.R. Martyn not out 66
S.R. Waugh not out 56
EXTRAS (B-4, NB-9) 13
TOTAL (for three decl, 62 overs) 284
FALL OF WKTS: 1-6, 2-146, 3-156.
BOWLING: Zaheer Khan 3-0-15-0 (1nb); Agarkar 12-3-45-1 (1nb); Nehra 19-1-89-1 (6nb); Harbhajan Singh 21-1-101-1; Tendulkar 2-0-9-0; Sehwag 5-1-21-0 (1nb).
INDIA (2nd Innings):
A. Chopra c Langer b Bracken 4
V. Sehwag c Martyn b Bracken 0
R.S. Dravid not out 43
V.V.S. Laxman not out 24
EXTRAS (NB-2) 2
TOTAL (for two wkts, 16 overs) 73
FALL OF WKTS: 1-4, 2-4.
BOWLING: Gillespie 5-1-17-0 (2nb); Bracken 4-1-12-2; MacGill 3-0-12-0; Bichel 4-0-32-0.
RESULT: Match drawn.
UMPIRES: S.A. Bucknor (West Indies) and R.E. Koertzen (South Africa).
TV UMPIRE: P.D. Parker (Australia).
MATCH REFEREE: M.J. Procter (South Africa).
MAN-OF-THE-MATCH: Saurav Ganguly.—Reuters