West Indies captain Brian Lara won the toss at Sabina Park and put Zimbabwe in to bat and he was rewarded with fine spells from his two opening bowlers.
Jerome Taylor bowled Friday Kasteni with the first ball of the second over, a delivery which cut back sharply off the seam and then the stumps tumbled at the other end with Vusi Sibanda inexplicably playing no shot to Daren Powell.
Zimbabwe, who tied their opening game against Ireland, were two for two and looking in real trouble.
Taylor struck again in the tenth over, Chamu Chibhabha beaten for pace as he was clean bowled to leave the African side still in difficulty at 31 for three.
Wicketkeeper-batsman Brendan Taylor and Stuart Matsikenyeri looked to lay down some foundations but after getting himself in, the experienced Matsikenyeri paid the price for a poor shot off Devon Smith, his underhit slog going straight to mid-on.
Taylor was joined at the crease by left-hander Williams and with Lara turning to spin -- utilising Chris Gayle and Marlon Samuels -- Zimbabwe made some steady, if unspectacular progress.
But just after Taylor completed his patient 50 in 121 balls, taking his side on to 142, he pressed the self-destruct button, run out at the non-striker's end after attempting an ill advised single.
With five down and nine overs left, Zimbabwe needed to step on the accelerator if they were to set West Indies a testing target and Williams and Elton Chigumbura (30) responded well with a 60-run partnership leaving their side with an outside chance.
Ireland and Pakistan complete the group with Pakistan already eliminated after losing to the Irish on Saturday.
Zimbabwe 202 for 5 in 50 overs (Sean Williams 70 n o, Brendon Taylor 50, Chigumbura 30 n o; Jerome Taylor 2 for 42, Powell 1 for 15, Dwayne Smith 1 for 28) Vs West Indies (yet to bat).