Chasing a daunting 295, Pakistan needed a tough 17 off the 50th over, but Akmal hit the second and third ball for sixes to give his team an unexpected win with a nine-ball 24 not out to overshadow Chris Gayle's brilliant century.
Gayle notched a 106-ball 113 to power his team to a challenging 294-9 in their 50 overs. Paceman Lionel Baker (3-47) nearly derailed Pakistan before Akmal and Fawad Alam (26 not out) changed the script.
Akmal walked in at the fall of Shoaib Malik's wicket whose enterprising 50-ball 66 nearly ended in vain but Akmal and Alam notched 33 needed off the last three overs to give Pakistan a 1-0 lead in the three-match series.
The second match will be played on Friday.
Gayle's counterpart, Malik hit six boundaries and a six during his 50-ball knock to anchor Pakistan's run-chase.
Besides Malik, opener Khurrum Manzoor scored a 89-ball 69 (five fours) in his only second one-day international while the experienced Younus Khan made a 62-ball 56.
Manzoor and Salman Butt (24) gave Pakistan a solid start of 64 before Baker bowled Butt who played on to a short delivery. Manzoor added 78 for the second wicket with Younus before Pakistan lost two quick wickets.
Manzoor edged Jerome Taylor to wicket-keeper, while Misbahul Haq (seven) was bowled by left-armer Nikita Miller, trying to reverse-sweep a straight delivery.
Baker returned for his second spell to have Younus and hard-hitting Shahid Afridi (four) before Taylor dismissed Malik -- all well caught in the deep -- to put West Indies in sight of a victory.
The West Indies were indebted to Gayle who scored his 17th one-day century and put his team a solid footing with a 125-run opening stand with Sewnarine Chattergoon (33) after winning the toss and electing to bat.
Ramnaresh Sarwan (55 off 61 balls) and Shivnarine Chanderpaul (36 off 33) also punished the lacklustre Pakistan bowling.
In the absence of Shoaib Akhtar, ruled out of the match because of a calf muscle injury, Pakistani bowlers struggled to get early wickets. Sohail Tanveer was the pick of the bowlers with 3-42.
Gayle took full advantage of some short bowling. He smacked four boundaries in one Abdur Rauf over and then greeted first-change Gul with two powerful sixes as he reached his half-century off just 36 deliveries.
Gayle, who reached a hundred with a single off Malik, failed to capitalise on a drop catch by Gul off his own bowling and pulled straight into the hands of Shahid Afridi at mid-wicket in the same over.
Sarwan took the baton from Gayle and reached his 50 with a delightful cover drive off Gul for his fifth boundary. He then fell to a smart leg-side catch by wicket-keeper Kamran Akmal off Afridi in the next over.
Chanderpaul and Xavier Marshall (26) gave the final touches as West Indies notched 71 off the last 10 overs.
Pakistan had to bring in Rauf for injured Akhtar, while the West Indies gave a one-day debut to Lionel Baker.