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Dhananjaya de Silva was 78 not out as Sri Lanka cruised to 155-2 in just 24.3 overs after Zimbabwe collapsed to 154.
Part-time bowler Asela Gunaratne took 3-21 for Sri Lanka, the last three Zimbabwean wickets, but the damage was already done as the home team was reduced to 50-6 in the 18th over.
Niroshan Dickwella made 41 from 38 balls with six fours and Sri Lanka raced to victory with a run rate of over six an over.
Peter Moor briefly held up the Sri Lankans with his 47 from 52 balls and captain Graeme Cremer was 31 not out.
Sri Lanka won with more than half their overs to spare as De Silva hit his 78 from just 75 balls with 12 fours.
The Sri Lankan seamers were too good for Zimbabwe on a green, seaming pitch, with Suranga Lakmal taking 2-19, Nuwan Pradeep 2-21 and Nuwan Kulasekara 2-23.
Four of Zimbabwe's top five failed to make double figures.
West Indies is also playing in the three-team ODI series and faces Sri Lanka in Harare on Wednesday.