West Indies were bowled out for 137 with one over to spare, chasing a mammoth total of 200 by Pakistan in the first Twenty20 International (T20I) in Karachi on Monday.
Rizwan smashed a 52-ball 78 with 10 boundaries — his 12th half-century and 11th this year — while Haider scored a career-best 68 to guide the hosts to 200-6 in their 20 overs.
The visitors were never in the hunt of the target as they were dismantled by a superior Pakistan bowling attack and folded at 137 in 19 overs.
Fast bowler Mohammad Wasim took a career-best 4-40 while spinner Shadab Khan grabbed 3-17.
Opener Shai Hope top-scored with 31 but became one of leg-spinner Shadab's two wickets in the same over, Shamarh Brooks being the other for five.
Odean Smith (24), Rovman Powell (23) and Romario Shepherd (21) also had good contributions but never threatened Pakistan.
This becomes Pakistan's 13th win in 19 Twenty20 internationals against West Indies, taking a 1-0 lead in the three-match series.
Pakistan were once again anchored by Rizwan who has had a phenomenal 2021 in Twenty20 international cricket, having already crossed 1,000 runs in the calendar year.
Rizwan and Haider added 105 for the third wicket after skipper Babar Azam fell without scoring and Fakhar Zaman made just 10, with West Indian bowlers getting early success.
It was a rare failure for Azam — ranked number one in T20I cricket — as he edged a sharp turning ball from spinner Akeal Hossein.
Zaman top edged Shepherd before Rizwan and Haider rescued Pakistan. Haider cracked four sixes and six boundaries in his 39-ball knock.
Mohammad Nawaz gave the final touches to the innings with a brisk 10-ball 30 not-out spiced with two sixes and three boundaries.
West Indies, hit with three Covid-19 positive tests among their T20I players, brought in Brooks and Devon Thomas from their one-day squad, giving Brooks a debut in the shortest format.
The remaining matches will be played on Tuesday and Thursday; both matches will be played at National Stadium Karachi.