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
Azhar Ali, Sarfaraz Ahmed lead respective sides in intra-squad warm-up game
Second group of Pakistan cricketers to leave for England on Friday
'Plans underway to stage remaining PSL matches this year' - PCB
Six players eligible to join Pakistan squad after second negative test in three days
Pakistan squad in England test negative for coronavirus
Match-fixing: PCB replies to concerns of Danish Kaneria and Saleem Malik
Shannon Gabriel officially added to West Indies Test squad
PSL Schedule Live Streaming and PSL 5 Matches Details
Younis Khan singles out Jofra Archer as the major threat for Pakistan
Asia Cup 2020 postponed to next year