Siakandar Raza lifted Zimbabwe from a precarious 23-4, followed by 59-5, after Sri Lankan left-arm spinner Rangana Herath rattled the visitors' batting with four early wickets.
Cremer's leg-spin and two crucial run outs left Sri Lanka reeling at 293-7 at stumps.
Ervine's career-best effort lifted Zimbabwe from a precarious 70-4 to 344-8 at stumps.
Arjuna Ranatunga on Friday demanded an investigation into the country's 2011 World Cup final defeat by India amid allegations of match fixing.
Chandimal will lead the islanders in a Test for the first time after Angelo Mathews resigned.
Sri Lanka appointed two new captains on Wednesday to replace Angelo Mathews, who resigned.
Zimbabwe notched their first win abroad in eight years after claiming the one-day international series against Sri Lanka 3-2
The series in also Zimbabwe’s first away win against a Test playing nation other than Bangladesh in 16 years – with New Zealand in 2001 being the last away victory
Zimbabwe clinched their second win of the series, courtesy Craig Ervine's quickfire 69 in a rain curtailed game, setting up the final ODI nicely on Monday
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