Rovers got back into the match when Cockayne profited from a Paul Cooke up-and-under to crash over and as conditions deteriorated the match remained on a knife-edge before Sheriffe ran KR out of town.
But Sri Lanka's upbeat mood was soon soured when Daren Powell, making the most of overcast conditions, bowled captain Marvan Atapattu off the inside edge for one and Lawson removed Sanath Jayasuriya for three to leave them on 7-2.
Slippery conditions caused by rain and the knowledge that the game was won took the edge off Australia's play in the closing stages, as their thoughts turned to next weekend's game with England in Melbourne and they sought to avoid injury against their hard-tackling opponents.
Her skates are chunks of steel as long as 13 feet (the crew changes skate length according to ice conditions), with an almost imperceptible curve along the bottom and a razor-sharp edge so that the skate bites hard into the ice.