Sent in to bat on a helpful pitch, Zimbabwe were restricted to 151 for nine from their allocation of 50 overs.
Justice Chibhabha hit five fours in the top score of 55 from 99 balls and featured in a vital stand of 64 for the second wicket with Zimbabwe captain Terrence Duffin, who scored 26.
Four West Indies bowlers - Jerome Taylor, Dwayne Bravo, Dwayne Smith and Chris Gayle - collected two wickets apiece.
The visitors looked set to make a competitive total when Chibhabha and Duffin added 64 for the second wicket.
But once they were removed, there was neither substance nor stability from the rest of the batting, as the Zimbabweans lost their last six wickets for 30 runs in the final 10 overs.
The visitors suffered an early setback, when opener Piet Rinke was caught at square leg for one in the second over.
With the West Indies bowlers gaining appreciable bounce and movement from the pitch, Duffin and Chibhabha played within their limitations to navigate Zimbabwe through the tough first half of the innings.
Duffin played a few crisp strokes through the off-side, where he is strongest, and Chibhabha offered steady support punctuating periods of solidity with the occasional stroke in anger.
Duffin had been fortunate in the fourth over when, on six, he gloved a rising ball from Taylor and wicketkeeper Denesh Ramdin spilled a straightforward chance.
Ramdin however, made no mistake the second time around just when it looked like Duffin and Chibhabha were getting ready to play their strokes.
Duffin was caught behind for 26 off Dwayne Smith edging a backfoot drive off the last ball of the 27th over.
Chibhabha continued to plod away and reached 50 when he sliced Taylor through backward point for two, but he became reckless after arriving at the milestone and was caught at long-off off Smith in the 37th over.
The series continues on Sunday when the two teams contest the second match at the same venue before heading to Georgetown for back-to-back matches on May 6 and 7.
They will play the first limited-overs international under lights in the Caribbean at Gros Islet's Beausejour Stadium on May 10 before the series ends in Port of Spain on May 13 and 14.