After winning the toss and batting first, the home side, featuring only four players expected to play key roles in the upcoming Ashes series, struggled to 8-133, after slumping to 5-43 in the 11th over.
Sri Lanka cruised to 3-133 in reply, winning with 21 balls to spare, inflicting Australia's first home defeat in 11 matches.
Clarke went into the game under pressure to retain his spot in the Australian side in the shortest form of the game, as he is averaging just over 20 in the format.
He promoted himself to the top of the order and the move very nearly backfired on the second ball he faced, with an inside edge just missing the stumps.
Clarke should then have been run out on two, when he was sent back by strike Dave Warner and was well out of his ground as the throw by Tillakaratne Dilshan from close range somehow missed.
The 29-year-old briefly looked as if he would capitalise on the good fortune, hitting Dilhara Fernando through mid-wicket for four, before lofting Muttiah Muralitharan, playing his last game in Perth, down the ground for six in the next over.
But on 16, his luck ran out when he lobbed a mistimed drive off Thisara Perera (2-22) down to long on, where a back-pedalling Dilhara Fernando -- who had started the Australian rot when he had Warner caught at mid-off for two -- misjudged the flight of the ball but stuck out his right hand to cleanly snare a remarkable catch.
Clarke had faced 19 balls, and his departure left the home side struggling at 2-22.
It got much worse though, with Perera then claiming Test opener Shane Watson for four and David Hussey (7) and Cameron White (8) both going cheaply as Australia collapsed to 5-43.
Brad Haddin (35) and Steven Smith (34) then came to the rescue, their 66-run partnership at least giving Australia a modestly competitive total to defend, before both fell in quick succession to Suraj Randiv, who impressed with 3-25 with his off-spinners.
The Sri Lankans had few problems overhauling the total, with captain Kumar Sangakkara unbeaten on 44 and Dilshan making 41.