De Silva made his highest ODI score off 75 balls as his side reached their target in less than half the allocated time after Zimbabwe were bowled out for 154 in 41.3 overs.
Niroshan Dickwella made 41 in the other significant contribution as Sri Lanka compiled 155 for two in 24.3 overs.
Earlier, the visiting seamers scythed through the top order to leave Zimbabwe 50 for six before Peter Moor (47) and captain Graeme Cremer (31 not out) fought back.
Sri Lanka meet West Indies at the same Harare Sports Club venue on Wednesday while Zimbabwe's next game is against West Indies in Bulawayo on Saturday.
(Reporting by Mark Gleeson in Cape Town; Editing by Tony Jimenez; mark.gleeson@thomsonreuters.com; +27828257807; Reuters Messaging: Reuters Messaging: mark.gleeson.thomsonreuters.com@reuters.net)
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