West Indies will need 212 runs to complete a 3-0 series clean sweep over Zimbabwe after restricting the visitors to 211 for nine in the final match at the National Stadium in Grenada.
The Caribbean side will start its reply shortly.
Veerasammy Permaul led the bowling for West Indies with three for 40 from his 10 overs.
Tino Best and stand-in captain Dwayne Bravo supported with two wickets apiece, while Sunil Narine ended with a wicket.
If the West Indies achieve the whitewash it will be the first over a Test-playing nation since they defeated Bangladesh 3-0 in 2004.
Following the ODI series, the teams will play two Twenty20 Internationals and two Test matches.