The West Indies were set a revised target of 223 off 39 overs after showers during the interval, and were 154 for more off 29.5 overs when more bad weather ended the match.
At that stage, the hosts were ahead by one run on the Duckworth/Lewis system, ensuring they avoided a sweep in the five-match series which Pakistan now leads 3-1.
The victory was West Indies' first over a top-seven nation since June 2009.
"We needed that. It's been a while since we hadn't won against a higher ranked opposition and to do that, the guys will take the positives," West Indies captain Darren Sammy said. "We created an opportunity today and it was good to see the guys pulling us through in the end."
Simmons struck four fours and three sixes to anchor the chase along with Ramnaresh Sarwan (28) and Darren Bravo (21).
Dwayne Bravo struck a crucial six off Pakistan captain Shahid Afridi to push West Indies ahead of the required total just before the rain had the final say. Left-arm seamer Junaid Khan led the visitors' bowling with 2-26.
Earlier, Mohammad Hafeez struck his second one-day century to form the backbone of Pakistan's challenging 248 for nine off 50 overs. The 30-year-old all-rounder lashed seven fours and three sixes in a career-best 121 off 138 deliveries. He shared a brilliant second wicket stand of 153 with fellow right-hander Asad Shafiq, who contributed 71. Shafiq cracked four fours off 102 balls.
But the innings subsided after that solid platform as the hosts fought back.
Legspinner Devendra Bishoo claimed 3-37 in his 10 overs, while there were two wickets apiece for seamers Dwayne Bravo (2-60) and Kemar Roach (2-67).
"We thought we would score about 270-275 but I think we really missed that chance," Afridi said. "We're disappointed because we missed an opportunity to score a higher score."
West Indies won the toss and got a good start when Roach claimed Ahmed Shehzad at 15-1. Shehzad top-edged a hook and Bravo took a brilliant catch running back 15 yards from square leg.
But Hafeez and the 25-year-old Shafiq laid the platform for a challenging total with their sound stand, although the Pakistan middle order couldn't supply the necessary tempo towards the end as Bishoo continued his fine rookie season.
Only tail-ender Tanvir Ahmed, with 18 off 12 balls, managed to reach double figures after Hafeez and Shafiq.
The West Indies chase, stalled initially by rain, got off to a terrible start when Junaid had Kirk Edwards caught behind first ball. But Simmons and Darren Bravo added 56 in 8.2 overs to revive the pursuit before Bravo fell to Junaid, slicing to third man at 57-2. Simmons and Sarwan then shared a partnership of 75 that tilted the balance to the West Indies.
But when both fell in successive overs, Pakistan were back in the hunt. Sarwan lofted Hafeez to long-off while Simmons skied Tanvir Ahmed to deep cover.
However, with the rain closing in, Dwayne Bravo swatted Afridi into the midwicket stands to seal the victory.
Mohammad Hafeez b Bishoo 121
Ahmed Shehzad c D.J. Bravo b Roach 6
Asad Shafiq c Simmons b D.J. Bravo 71
Shahid Afridi c Rampaul b Roach 8
Misbah-ul-Haq b Bishoo 5
Hammad Azam c Roach b Bishoo 1
Usman Salahuddin run out 5
Mohammad Salman run out 0
Tanvir Ahmed b D.J. Bravo 18
Saeed Ajmal not out 5
Junaid Khan not out 1
Extras (lb1, w5, nb1) 7
Total (9 wkts, 50 overs) 248
Fall of wickets: 1-15 (Ahmed Shehzad, 4.3 overs); 2-168 (Asad Shafiq, 38.2); 3-182 (Shahid Afridi, 40.4); 4-210 (Misbah-ul-Haq, 43.5); 5-219 (Mohammad Hafeez, 45.1); 6-220 (Hammad Azam, 45.4); 7-220 (Mohammad Salman, 46.1); 8-236 (Usman Salahuddin, 48.4); 9-244 (Tanvir Ahmed, 49.3)
Bowling: Roach 10-0-67-2 (nb1, w1); Rampaul 10-2-37-0 (w1); D.J. Bravo 10-0-60-2 (w2); Sammy 10-0-46-0 (w1); Bishoo 10-0-37-3
West Indies (target: 154 off 29.5 overs):
Lendl Simmons c Salahuddin b Tanvir Ahmed 76
Keith Edwards c Mohammad Salman b Junaid Khan 0
DM Bravo c Tanvir Ahmed b Junaid Khan 21
Ramnaresh Sarwan c Junaid Khan b Mohammad Hafeez 28
Marlon Samuels not out 8
DJ Bravo not out 11
Extras (w9, nb1) 10
TOTAL (4 wkts, 29.5 overs) 154
Fall of wickets: 1-1 (Edwards, 0.2 overs); 2-57 (D.M. Bravo, 8.4); 3-132 (Sarwan, 24.3); 4-135 (Simmons, 25.4)
Bowling: Junaid Khan 6-0-26-2 (w1); Tanvir Ahmed 6-0-45-1 (nb1); Shahid Afridi 6.5-0-32-0 (w7); Saeed Ajmal 4-0-16-0; Mohammad Hafeez 6-0-26-1 (w1); Hammad Azam 1-0-9-0
Result: West Indies won by one run (D/L Method)
Series: Pakistan lead five-match series 3-1