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
Wahab Riaz, Faheem Ashraf included in 20-man shortlist for England Tests
Sohail Khan bags five wickets as Pakistan's leading batsmen flounder
Team Green put on improved batting display after Naseem Shah shines again
'Plans underway to stage remaining PSL matches this year' - PCB
'Disappointed over England tour snub given my experience of county cricket' – Junaid Khan
Haris Rauf set to join Pakistan squad in England after returning two negative tests
Bringing Mohammad Amir back is a positive move, says Waqar Younis
Broad takes 500 Test wickets, Woakes bags five as England reclaim Wisden Trophy
Mohammad Amir departs for England tour after testing negative twice for Covid-19
Umar Akmal's ban reduced to 18 months; eligible to return in August 2021