Pakistan needed 178 to win and sweep the two-match series after being reduced to 76-4 at stumps on the second day but lost two quick wickets when Saud Shakeel (13) and Kashif Ali (1) were removed cheaply by Kevin Sinclair and Jomel Warrican.
Mohammad Rizwan gave the hosts a fighting chance, scoring 25 runs off 62 deliveries, before the wicketkeeper-batter was sent packing in the 42nd over by Warrican, who did the bulk of the damage for the West Indies with five wickets in the second innings.
Reduced to 122-8, Pakistan's chase fizzled out when Gudakesh Motie removed Noman Ali and Warrican struck again to take out Sajid Khan.
"Just the variation of pace and hitting the same length over and over," said Warrican, who was named Player of the Match and the Player of the Series. "Consistency is the key to everything I do."
The hosts won the first test, also in Multan, by 127 runs.
"We haven't played in Pakistan for a number of years, but we haven't won here in a while, so to come here and do it as a young group is incredible," West Indies captain Kraigg Brathwaite said.
"On this pitch, there's a ball with your name on it around the corner. We did that with the bat in the second innings, and it was good to see. It was a good experience.
"When you get on better pitches, you can have a similar mindset and it will help you in the long run."
