Captain Ricky Ponting batted for six hours for 156 but was dismissed with 24 balls to go, leaving Brett Lee and Glenn McGrath to see Australia to safety.
Man of the match Ponting put on 81 with Michael Clarke (39) and 76 with number nine batsman Shane Warne (34).
Andrew Flintoff took 4-71 but could not
claim the vital last wicket.
After two of the most exciting Tests in history - this match following England's two-run win at Edgbaston - the series moves to Trent Bridge for the fourth Test of five with everything to play for.
I worked really hard but I thought I'd cocked it up at the end
Ricky Ponting More Australia reaction
It was the first time in 10 years that Australia have been forced to bat out a draw against their Ashes rivals.
And the tension was at its height as a crowd of 21,000 roared Flintoff on as he came in to bowl the penultimate over to Lee with seven fielders in the slip cordon.
Lee saw that out and punched the ground in triumph as he pushed a full toss from Harmison to the fine leg boundary to save the match.
Australia were 24-0 overnight, needing to bat out a minimum of 98 overs to salvage a draw, or score a record 423 for victory, while England needed 10 wickets.
And at times during an adrenaline-fuelled final day, all three results seemed possible.
The series is really well poised and we are looking forward to the last two Tests now
Michael Vaughan More England reaction
England's bid for victory began in ideal fashion as Matthew Hoggard got his first delivery, in the second over, to seam away from Justin Langer and induce an edge behind.
The momentum moved slowly in Australia's direction as Ponting survived a difficult start to secure the first century by an Australian in the series so far.
With Clarke in tandem with his captain, Australia could really consider the prospect of snatching a win as England began to look bereft of ideas.
Warne survived on 30, when Hampshire team-mate Kevin Pietersen put down a difficult chance at midwicket.
But he appeared to have helped Ponting secure the stalemate before a dramatic dismissal that second slip Andrew Strauss parried to a diving Geraint Jones with 59 balls remaining.
When Ponting was the ninth wicket to fall, victory for England appeared a formality despite the ticking clock, but Lee and McGrath stood firm.
Ponting survived a stumping chance off Ashley Giles while in single figures, and took a good while to settle again before going to make his highest score against England.
England's Steve Harmison shows his frustration
A gritty stand of 71 with Matthew Hayden was undone by a brilliant piece of planning from Flintoff, who repeatedly angled deliveries across left-hander Hayden before moving over the wicket to take out his leg stump.
Neither Damien Martyn, controversially given out lbw for 19 when replays showed an inside edge onto his pads, nor Simon Katich were able to capitalise on comfortable starts.
Flintoff dismissed Katich for 12 and Adam Gilchrist for four in a fine mid-afternoon spell, both men edging behind square with ill-advised wafting shots outside off stump.
Clarke's participation in the match had been limited to two overs in the field and 19 minutes at the crease in the first innings.
But he showed few signs of the back trouble that has seen him confined to his hotel bed for much of the match.
Both he and Ponting took particular pleasure in taking on Giles, driving through the off side with abandon to force England to withdraw the spinner from the attack.
Clarke did not even have a shot to offer Jones, whose fourth ball of a long-awaited new spell swung in wildly to take out his off stump.
But England then took the second new ball, allowing Warne crucial time to find his feet and extend Australia's defence just long enough.
The Third Ashes test ended in a draw as England ended 1 wicket short of victory. A captain's innings of 156 by Ricky Ponting helped Australia save the game on the fifth day. 

When Ponting was dismissed with four overs to go a tense endgame ensued as England sought the final wicket but Brett Lee and Glenn McGrath fought to deny them that prize.

Earlier in the game the batsmen held sway as the third test saw the first centuries of the series from England's Michael Vaughan (166) and Andrew Strauss (106). 

With England setting Australia an unlikely 423 to win in just over a day it was Ponting's 156 that was the most significant contribution as he batted for six hours to deny England a second consecutive victory.

The series remains at 1-1 with two matches to play.

Scores: England 444 and 280-6 dec. Australia 302 and 371-9