The Sri Lankans beat the Prime Minister's XI comfortably on Wednesday in Canberra, but Tasmania thrashed them by seven wickets in their one-day match.
After winning the toss and batting, the Sri Lankans failed to bat out their overs in making 183 for nine, with Jayasuriya retiring hurt on eight.
In reply, Tasmania cruised to 184 for three, winning with more than 13 overs to spare.
Jayasuriya, in his last tour of Australia, was hit in the jaw when he top-edged a delivery from Tasmanian opening bowler Tim MacDonald in the eighth over.
The 38-year-old needed six stitches and was taken to a local hospital for precautionary x-rays, but is expected to be available for Sri Lanka's opening tri-series clash with India in Brisbane on Tuesday.
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Captain Mahela Jayawardene was the only Sri Lankan to impress with the bat, making 51 from 59 balls.
However, star wicketkeeper-batsman Kumar Sangakkara failed for the second time in three days, falling for a second-ball duck to Tasmanian pacema