When man-of-the-match Kemar Roach took the first three wickets to fall, Pakistan were 15 for three.
In the end they were all out for 170 with only captain Misbah-ul-Haq, whose 96 not out was his highest score in 118 one-day internationals, and Nasir Jamshed (50) making it to double figures.
But the West Indies suffered a collapse of their own before tailender Roach hit the winning boundary with more than nine overs remaining.
On the ground where they won the 2004 Champions Trophy, West Indies slumped to 15 for two after giant left-arm quick Mohammad Irfan removed Johnson Charles and Darren Bravo.
Chris Gayle typically drove Irfan, world cricket's tallest player, for six, only to be bowled for 39 trying to slog off-spinner Saeed Ajmal.
The match was in the balance at 81 for four after Ramnaresh Sarwan was caught behind off a rising delivery from left-arm quick Wahab Riaz.
Kieron Pollard, known as a big-hitter, took 18 balls to get off the mark as the West Indies crawled towards victory in front of a crowd of more than 20,000.
But when Pollard was caught behind off Riaz for a 58-ball 30, his side were still 34 runs short of victory.
West Indies captain Dwayne Bravo, who took 36 balls without a boundary in labouring to 19, was unable to see his side to victory, falling lbw to Ajmal.
Sunil Narine soothed West Indies' nerves with two fours.
But when he was caught behind off Irfan, West Indies were still six runs adrift before Roach slammed the clinching boundary off Junaid Khan.
Earlier, after Roach's initial burst, off-spinner Narine took three wickets for three runs in 10 balls.
Misbah survived two close calls off successive balls on nought that, had they gone against him, would have left Pakistan 19 for four.
But the 39-year-old went on to surpass his previous ODI best of 93 not out against New Zealand at Napier in 2011.
Dwayne Bravo won the toss and six balls later took a brilliant diving second slip catch to dismiss Imran Farhat off Roach.
Hafeez was clean bowled middle stump by Roach and when Asad Shafiq fell for nought, after an uppercut went straight to third man, the paceman had taken three for five in 14 balls.
Misbah, on nought, survived a West Indies reviewed appeal for lbw from Roach.
Next ball Roach thought he had Misbah caught behind with umpire Steve Davis giving him out.
But square leg umpire Nigel Llong told Misbah to wait while the catch was checked on replay and wicket-keeper Denesh Ramdin was ruled not to have had full control of the ball before fumbling it.
Jamshed, soon after reaching fifty, holed out off Narin, who then had Shoaib Malik (nought) chipping to Bravo at short mid-wicket and Akmal caught behind by Ramdin.
Misbah, on 67 when last man Irfan came in, drove Rampaul for a straight six and went into the nineties with a similar shot off Narine.
But he was denied a maiden century when Irfan mistimed a slower ball from Rampaul to Bravo at short mid-on. Misbah faced 127 balls including three sixes and five fours.
Pakistan and West Indies are in the same group as India and South Africa, with only the top two sides going through to the semi-finals.
India beat the Proteas by 26 runs in the tournament opener in Cardiff on Thursday.
Pakistan next play South Africa at Edgbaston on June 10 with the West Indies facing India at The Oval on June 11.
