Dickwella (116) and Gunathilaka (87) put together 209 runs after the hosts elected to bat first -- becoming the first pair in ODI history to score back-to-back double century partnerships.
The left-handed batting duo had put on a 229-run match- winning stand in the previous ODI on Thursday at the same venue.
While Dickwella hit his second successive century with a commanding 116, Gunathilaka missed out on what could have been his second ODI ton after being bowled for 87.
Zimbabwe off-spinner Malcolm Waller got the two prized wickets in successive overs to pull things back for the visitors.
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Paceman Chris Mpofu also got two wickets to rattle the Sri Lankan middle-order as the hosts slipped from 216-1 to 263-5.
Skipper Angelo Mathews then lifted the total with his 40 -ball 42, with help from Wanindu Hasaranga (19 not out) during their 37-run partnership for the seventh wicket.
The hosts, already leading Zimbabwe 2-1, are looking to take an unassailable lead in the five-match series.