Sri Lanka, trailing Australia by 304 runs on the first innings, were bowled out for 103 with Kumar Sangakkara retiring hurt and two other players unable to bat because of injuries.
Sri Lanka succumbed in just 24.2 overs and 130 minutes and now have to regroup amid their catalogue of injuries for the third and final dead rubber Test, starting in Sydney next Thursday.
Australian paceman Mitchell Johnson was named man-of-the-match with six wickets and an unbeaten 92.
Australia won the opening Test in Hobart by 137 runs.
Match scores: Sri Lanka 156 and 103-7; Australia 460