Dwayne Smith smashed 29 off seven balls as the West Indies recovered from a poor start to post 164-8 against Bangladesh in the Twenty20 world championships here.
The West Indies, sent in to bat on a drying wicket at the Wanderers, struggled to 104-3 in 15 overs before the lower order added 60 valuable runs in the last five overs.
Smith plundered four sixes and a boundary before being dismissed off the last ball of the innings in a match West Indies must win to stay afloat after losing to South Africa on Tuesday.
The match was delayed by an hour due to a wet pitch caused by excessive watering overnight by the ground staff, but there was no reduction in overs.
Chris Gayle, who hammered the first-ever Twenty20 century in the previous match, fell to the third ball of the innings when he cut Syed Rasel to Alok Kapali at point.
Left-armer Rasel kept the runs in check with a superb spell of 1-10 in four overs even as Shivnarine Chanderpaul and Devon Smith put on 95 for the second wicket.
Chanderpaul made 37 off 31 balls with three fours and two sixes, while Devon Smith top-scored with 51 off 52.
Marlon Samuels launched the late charge with two sixes and two boundaries in one over of Bangladesh captain Mohammad Ashraful before holing out off the over's final delivery.
Dwayne Smith hammered three consecutive sixes in another over from Ashraful, who conceded 55 runs in his spell.
Left-arm spinner Shakib Al Hasan finished with 4-34, including three wickets in the last over of the innings.
Bangladesh, playing their first match in the tournament, face a victory target of 8.3 runs an over.