Set a revised target of 189 off 31 overs after the West Indies had totalled 261 for seven off 49 overs, the Pakistanis reached 189 for four with six balls to spare with Mohammad Hafeez top-scoring on 59.
They lead 2-1 in the series with one match tied ahead of the fifth and final game in St Lucia on Wednesday.
"I am very pleased. We were looking to exploit the pitch but the rain came early," said Pakistan skipper Misbah- ul-Haq who was unbeaten on 53.
"It was like a normal T20 game, Hafeez and I wanted to play normal cricketing shots. It was the case of not panicking. The team will gain from the momentum today."
Marlon Samuels, with an undefeated 106, was the West Indies top scorer.
"West Indies cricket is still on the rise so we want the fans to stay with us," he pleaded.
"I set high standards and I'm still in good nick. If you look at my career I have never failed consistently. The coach has been telling the players to give ourselves a chance. There is some fire burning inside me so I had to let it off."