Batting first, Zimbabwe were restricted to 130 for eight with West Indies paceman Tino Best picking up three for 18 in his four overs.
Best removed both Zimbabwe openers Vusi Sibanda (13) and Hamilton Masakadza (9) cheaply as the tourists struggled at 28 for three.
Craig Ervine (34) and Malcolm Waller (49) held together the Zimbabwe innings with a 60-run partnership in ten overs but the lower middle order were unable to capitalise.
In response, Simmons was ably supported by Johnson Charles, the pair putting on 30 inside four overs before Charles was trapped lbw by Chris Mpofu.
Mpofu then removed Darren Bravo for a duck, the left hander's attempted pull looped up to Chamu Chibhabha, to offer Zimbabwe a brief opening.
But Bravo's brother Dwayne came in and struck 38 from 30 balls as he and Simmons, with their 85 run partnership, saw the Caribbean team to victory with 23 balls remaining.
The second and final game of the series will also be played at the Sir Vivian Richards stadium in North Sound on Sunday.
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