Windies struggled to 219 all-out in its first innings but leg-spinner Bishoo made use of the spin-friendly pitch at Queens Sports Club to claim a fourth five-wicket haul and put the tourists in a position of strength.
Chase's dismissal just after tea to Sikandar Raza, another spin bowler, set off the West Indies collapse.
The first-ever four-day Test, to be played between South Africa and Zimbabwe, will be played with the pink-ball and under lights.
West Indies will begin their tour with a three-day warm-up game against Zimbabwe A, which begins on October 15 at the Bulawayo Athletic Club.
At stumps, Sri Lanka were 170/3, with Kusal Mendis (unbeaten at 60) and former skipper Angelo Mathews (unbeaten at 17) batting at the crease.
Sikandar Raza pulled visitors out from troubled waters to help Zimbabwe to notch up an important 262-run lead at stumps on the third day of the one-off test against Sri Lanka.
Sri Lanka trail by 63 runs as Zimbabwe's skipper Cremer picked up three crucial wickets on Day 2 to put visitors ahead.
Ervine (151*) knitted crucial partnerships with Sikander Raza (36) and Malcolm Waller (36) to pull Zimbabwe out of initial trouble.
After being reduced to 70/4 at one stage, batsman Craig Ervine (151 not out) revived the visitors with a fine batting display to take Zimbabwe's total to 344/8 at stumps on Day 1.
Angelo Mathews has stepped down as Sri Lanka captain after the morale-shattering series defeat against Zimbabwe where the Islanders lost the five-match ODI rubber 2-3.
After a heavy loss to Zimbabwe, Sri Lankan skipper Angelo Matthews says that the team altogether have to work against the visitors in a one-off Test match
It was Zimbabwe's first ODI series victory over Sri Lanka in six attempts.
Sikandar Raza starred with both the bat and ball to help Zimbabwe edge out Sri Lanka by three wickets and clinch a historic series victory in the fifth One-day International.
Danushka Gunathilaka and Niroshan Dickwella scored their maiden international centuries to help hosts beat Zimbabwe by eight wickets in the third one-dayer.
With the win, the hosts have levelled the series 1-1 after Zimbabwe won the first match by six wickets.
Zimbabwe made 322/4 with 14 deliveries to spare in reply to Sri Lanka's formidable 316/5, in the biggest successful run chase in the country.
India today survived a scare from Zimbabwe, beating them by 3 runs in the final match of the series, sealing the three-match tournament 2-1. Chasing the target of 138, Zimbabwe managed to score 135 runs for 6 wickets in 20 overs.
Harare: India thrashed Zimbabwe by 10 wickets in the second T20 International to draw a level in the three-match series 1-1 at the Harare Sports Club today. Chasing a paltry target of 100, openers Lokesh
Zimbabwe won the toss and elected to bat in the second Twenty20 International against India at the Harare Sports Club here on Monday.
An Indian national was booked regarding the alleged rape in Zimbabwe but he is not a member of the Indian Cricket Team, official sources said today.
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