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Chapman top-scored for the home side with 42 from 29 balls as they reached 186 for five from their 20 overs after being asked to bat.
In reply, Sri Lanka managed 141 all out, led by Kusal Perera’s 48 from 35 balls.
Otago quick Jacob Duffy took career-best figures of four for 15 for the home team which wrapped up the three-match series 2-0.