Chasing 183 for victory at Eden Gardens on Saturday, Scotland were 5-132 after 16 overs before Shepherd bowled his four-wicket over, running through the lower-order.
After conceding one run with the first ball of the over, Shepherd had Matthew Cross caught at point and Michael Leask snared near long-on before the bowler went on to hit the top of Oliver Davidson's off-stump to complete his second hat-trick in T20 Internationals.
Next man in, Safyaan Sharif, survived the next delivery but fell immediately afterwards, lofting one to Jason Holder at mid-off.
Scotland, who entered the tournament after Bangladesh refused to tour India citing safety concerns, were all out for 147 in 18.5 overs.
Shepherd finished with the superb figures of 5-20, while Holder claimed 3-30.
Put in to bat, West Indies had earlier posted 5-182 with Shimron Hetmyer (64) providing the bedrock with a 36-ball knock that included six sixes.
"That was phenomenal. I think he was going to get it to be honest," Hetmyer said of Shepherd, while celebrating his player-of-the-match medal.
"It's not often you see a guy get five wickets and a hat-trick."
