The hosts, chasing 227, were 21 runs short of their target when bad light forced the players off the field with four overs remaining.
That deprived a packed crowd of a thrilling finish and left England to settle for a 3-0 win in the series.
Captain Michael Clarke had declared Australia's second innings on 111 for six and set England a challenging target in a bid to force a consolation victory.
However, it was the hosts who went close to sealing their first 4-0 victory in a home Ashes series.
England started their run chase positively and Alastair Cook hit two fours in the first over bowled by Ryan Harris.
Joe Root, on 11, edged Harris to wicketkeeper Brad Haddin before Cook and Jonathan Trott shared a fluent second-wicket partnership of 64 to lay a solid platform.
Cook was trapped lbw by James Faulkner for 34 and Pietersen strode to the middle in a perfect situation to display his attacking talents.
The tall right-hander struck his first boundary off his fourth ball and immediately injected urgency into the run chase, creaming Peter Siddle through the covers for four and flicking him to fine leg for another.
Pietersen and Trott posted their 50 partnership off 48 balls and Pietersen got to his own half-century from just 36 deliveries, including nine fours.
With the crowd sensing a famous victory, Trott also passed 50 before Pietersen fell with the score on 163, well caught by David Warner running round the long-on boundary off Harris.
Trott was trapped lbw by Faulkner for 59 but Ian Bell and Chris Woakes kept the momentum going and England needed 36 from the last six overs.
Bell was run out for 17 by Starc's direct hit and, with four overs remaining and England on 206 for five, the umpires ordered the players off the field to a chorus of boos.
The result was confirmed shortly afterwards and the awards ceremony took place in rapidly fading light.
It was an unexpected finale to the match after Saturday was washed out by rain, England starting the final day on 247 for four and needing 46 runs to avoid the follow-on.
Woakes, on 25, soon edged a good-length ball from Harris straight to Clarke at second slip but Matt Prior played positively from the start, clipping Siddle through mid-wicket for two to take England to the follow-on target of 293.
Bell, continuing his rich vein of form to reach an assured 45, was unlucky to be out when he flicked Faulkner down the leg-side and was well caught by wicketkeeper Brad Haddin.
Starc uprooted Stuart Broad's middle stump but Graeme Swann immediately went on the offensive, dancing down the pitch to hit off-spinner Nathan Lyon straight for six and lift England to 350 for seven at lunch.
Prior, on 47, skied Faulkner to mid-on where Starc ran round to take a fine diving catch and James Anderson edged the same bowler to Haddin who took a record-equalling 28th catch of the series.
Swann's breezy innings ended on 34 when he was bowled by Faulkner who completed figures of four for 51 in his first Test.
Australia shuffled their order in a bid to make quick runs but the move back-fired.
David Warner was out for 12, Shane Watson 26, Haddin for a first-ball duck and Faulkner for 22 as Australia stumbled to 67 for four.
Broad then dismissed Steve Smith and Harris before Clarke, who made 28 not out, and Starc, 13 not out, batted through to tea when the captain declared.
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- Alastair Cook
- Jonathan Trott