As a result, the Aussies will retain a 1-0 lead series lead with two games left to play.
England's first innings got off to a bad start, as a terrible mix-up between Pietersen and Carberry saw the latter run out by Clint McKay for just one run.
Pietersen (6) was the next to go, with George Bailey taking the catch off the bowling of Mitchell Johnson to leave the Three Lions 26-2.
Johnson thought that he had Jonathan Trott trapped lbw, but the decision was overturned on appeal, with hawkeye showing that the ball pitched outside leg stump.
The South Africa-born batsman survived on review once more before Joe Root (10) eventually became the Aussies' third victim, as he trudged off after being caught and bowled by Adam Voges.
Rain stopped play shortly after and, although the umpires initially slated an 8pm cutoff for play to resume, the call was made to abandon just after 7pm.
The fourth ODI takes place at Cardiff on Saturday, before the series wraps up at the Rose Bowl, Southampton, on Monday.