Munsey hit a string of boundaries including three straight fours off Alzarri Joseph, whose first over at a T20 World Cup cost 15 runs.
The 45-minute rain break seemed to hit the batting momentum as Jason Holder bowled Jones for 20 soon after play resumed and then sent back Matthew Cross for three in his next over.
Munsey, named man of the match, stood firm and attempted to rebuild with skipper Richie Berrington, who got a good start but fell on 16 off Joseph.
Munsey, playing his 54th T20 for Scotland, reached his first T20 World Cup fifty after a cameo by Calum MacLeod, who smashed 23 off 14.
Munsey finished with a flourish as he hit three fours in a 15-run 20th over from Odean Smith.
In reply for West Indies, Kyle Mayers started aggressively with three boundaries but mistimed a hit to be caught out by Munsey off pace bowler Josh Davey. He made 20.
Evin Lewis and Brandon King hit back with a flurry of boundaries in their attempt to get quick runs in the first six overs of powerplay -- when only two fielders are allowed outside the inner circle.
But their stay was shortlived as left-handed Lewis fell for 14 and King was bowled by Watt, who returned figures of 3-12 from his four overs.
The two-time champions slipped further at 62-4 when off-spinner Michael Leask bowled skipper Nicholas Pooran in single figures.
Scotland's bowlers kept chipping away as the rest of the West Indies batting caved in, despite a valiant 38 by Holder, who was the last man out.