Pakistan were reeling at 61-4 following Tonge's incisive opening spell, but teenager Umar Akmal helped his side surpass a 134-run target with a responsible 41 not out in the day-night match on a lively track.
Tonge finished with 4-25 off 10 overs in only his third one-dayer.
The under-strength West Indies were also well-served by wicket-keeper Chadwick Walton, who took four catches.
Tonge struck in his opening over when he bowled Imran Nazir and then had Kamran Akmal, Shoaib Malik and Mohammad Yousuf caught behind to put pressure on Pakistan.
Yousuf (23), dropped on one by Darren Sammy in the slips off Tonge, and Malik (23) looked set to put Pakistan in a comfortable position before falling in the space of seven runs.
Man-of-the-match Akmal, 19, also survived a nasty blow on his fingers off a Tino Best beamer in the later part of his knock, but kept his cool under pressure. He hit six fours.
Shahid Afridi, leading in his first one-day international, remained unbeaten with 17. He added 58 crucial runs for the unfinished sixth wicket with Akmal.
Pakistan will now clash with arch-rivals India in their next match at Centurion on Saturday. Defending champions Australia are the other team in Group A, with the top two sides making it to the semi-finals.
Teenage paceman Mohammad Aamer and Umar Gul earlier grabbed three wickets apiece to restrict the West Indies to a small total.
Left-arm seamer Aamer, 17, finished with an impressive 3-24 in only his sixth one-day international, while paceman Gul bagged 3-28 as the West Indies failed to last their quota of 50 overs.
Lower-order batsman Nikita Miller top-scored with a gutsy 51 for his maiden half-century in one-day internationals. He smashed one six and six boundaries in a 57-ball knock.
Sammy (25) and Devon Smith (18) were the others to reach double-figures in a dismal performance after the West Indies elected to bat.
The West Indies were in danger of falling below the 100-mark when they are struggling at 47-7 before adding 86 for the last three wickets, thanks to Miller and Sammy.
The West Indies are without key players Chris Gayle, Ramnaresh Sarwan, Shivnarine Chanderpaul and Dwayne Bravo following a contract row between the players and their cricket board.
Aamer struck with his sixth delivery when he held a return catch to dismiss Dale Richards. He kept pressure on the batsmen with a lively pace, taking two more wickets.
There was no respite from pace for the inexperienced West Indies as Aamer was brilliantly backed by Gul. Off-spinner Saeed Ajmal was the other notable wicket-taker with 2-16.