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Needing only five runs to win, opener David Warner hit Ramesh Mendis for a four and followed it with a six to seal Australia's victory in four deliveries.
No spectators were in the stand at the time, with the Australian team only just arriving at the ground.
England bowled out Sri Lanka for 203 before stretching their lead to 177 runs on the second day of the opening Test.
England declared their second innings on 322 for six to set Sri Lanka an improbable 462-run victory target.
Results 1-4