Perera claimed four wickets with his medium-pace as Zimbabwe survived 44 overs after electing to bat first.
Wicketkeeper-batsman Brendan Taylor top-scored with 58.
Perera, who ran through the Zimbabwe top-order including Taylor's wicket, was ably supported by fellow paceman Nuwan Pradeep (3-28).
Left-arm wrist spinner Lakshan Sandakan took wickets before Pradeep wiped off the Zimbabwe tail including the prized wicket of skipper Graeme Cremer for 34.
Sri Lanka are still searching for their first win in the series after losing their matches against Zimbabwe and hosts Bangladesh.
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