Chasing a revised target of 191 from 30 overs, Zimbabwe had reached 72 for two off 12.1 overs, and were ahead of the required scoring rate under the Duckworth-Lewis Method, when the second shower of the afternoon drenched the ground, forcing the umpires to abandon the remainder of the match.
West Indies hold a 4-0 lead in the seven-match series, after back-to-back victories by five wickets and 98 runs at St. John's, an 82-run win last Sunday at Georgetown, and a 10-wicket triumph last Wednesday at Gros Islet.
The third ODI scheduled for Georgetown was cancelled without a ball being bowled while the final match is here on Sunday.
Makeshift opener Morton had struck 12 fours and one six in 109 from 150 balls, as West Indies totalled 263 for six from their allocation of 50 overs after choosing to bat in ideal conditions.
Ramnaresh Sarwan supported with five boundaries in 54 from 62 balls and added 134 for the second wicket with Morton.
It took a late charge from left-hander Shivnarine Chanderpaul and Carlton Baugh, Jr., in an unbroken stand of 57 for the seventh wicket to beef up the Windies' total.
Chanderpaul struck two fours and two sixes in an unbeaten 51 at better than a run-a-ball and Baugh clouted three fours and one six in 25 not out from 15 balls.
Zimbabwe were seven without loss and into the second over of their reply when rain forced them off the field.
When play restarted, Zimbabwe lost two wickets in the space of nine balls that left them on 42 for two.
Captain Terrence Duffin was caught behind for 14 off Marlon Samuels trying a reverse sweep in the sixth over, and Piet Rinke, batting at three was run out when he failed to beat Brian Lara's throw from square leg.
Taylor came to the wicket and announced himself with a six over long off off Corey Collymore and was just getting into the swing of things with Vusimuzi Sibanda when the showers interrupted for the second and final time.
Earlier, Morton had batted with enterprise before on-drive for his eighth boundary off Gregory Strydom carried him to his 50.
But he and the rest of the batsmen were then kept in check by purposeful bowling from spinners Ryan Higgins and Prosper Utseya.
Tawanda Mupariwa had made the breakthrough in the fifth over, when left-handed opener Chris Gayle was bowled for two to leave West Indies 15 for one.
Sarwan came to the crease and was eventually caught behind in the 31st over off Higgins, the same way Lara was dismissed six overs later to give the leg-spinner two wickets for 39 runs from his allotment of 10 overs.
In the final push inside the last 10 overs, West Indies lost three wickets, including Morton, but not before he drove Anthony Ireland straight for a boundary to reach the century mark.
Morton was eventually caught at long on off the same bowler, and Marlon Samuels and Dwayne Smith were dismissed in the space of 12 balls to leave West Indies 206 for six leaving Chanderpaul and Baugh to carry the home team the rest of the way.