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.
skipper Babar Azam praised the effort from his batsmen.
"Rizwan and Haider played handy knocks and the way Nawaz finished was outstanding," said Azam.
"Our spinners bowled well and put them under pressure."
West Indian skipper Nicholas Pooran admitted his bowlers gave extra runs.
"I think we gave away 20 runs more in the field and there were a few boundaries off the edges too," said Pooran.
"I loved the effort and energy from the guys tonight. We are a young side but it all comes down to execution."
Pakistan were once again anchored by Rizwan who has 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 spices 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 are on Tuesday and Thursday, also in Karachi.