England were 35 for three at lunch on the fifth and final day, having lost captain Alastair Cook, Jonathan Trott and first-innings century-maker Kevin Pietersen.
They needed a further 2987 runs to reach their victory target of 332 after Australia captain Michael Clarke declared on his side's overnight 172 for seven.
Joe Root, dropped on four, was 13 not out and Ian Bell two not out.
Clarke had been angry when the umpires took the players off the field for bad light on Sunday.
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Harris though brought one back late into left-hander Cook's front pad to have him lbw for nought, with England yet to score a run.
Cook reviewed Tony Hill's decision but there was nothing to suggest he got an inside edge and, with tracking technology indicating the ball had pitched in line, the New Zealand umpire's decision was upheld.
Trott survived an lbw appeal from Harris when on nine, a decision the Australians reviewed only to be defeated by a marginal 'umpire's call' verdict after replays showed the ball taking the outside part of leg stump.