The captain made a 57-ball 104 not out, smashing five sixes and 12 fours in a superb display of hard and clean hitting to help his team post a challenging 198-3 in the day-night match at the Pallekele International Stadium.
Australia were restricted to 163-8, with opener David Warner top-scoring with a 31-ball 53 with the help of two sixes and six fours.
Sri Lanka virtually wrapped up the match when they reduced Australia to 63-4 in the opening nine overs, with debutant off-spinner Dilruwan Perera doing the maximum damage with three wickets.
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Dilshan needed 16 runs to complete his hundred in the last over bowled by paceman Mitchell Johnson, but struck two sixes and as many fours. His second fifty came off just 16 deliveries.
The Sri Lankan captain and Jeevan Mendis (29 not out off 19 balls) plundered 104 runs in the last 7.3 overs to help their team set a stiff target.
"I am really satisfied. Earlier on I batted a bit slowly but then played big shots later. It was a good toss to lo