Left-arm spinner Nawaz then achieved career best bowling figures of 4-19 as the visitors were shot out for 155 in 32.2 overs.
The win gives Pakistan an unbeatable 2-0 lead in the three-match series and their 10th consecutive ODI series win over the West Indies.
Pakistan’s last ODI series defeat to the West Indies was back in 1991. The two wins give Pakistan 20 valuable points in the ODI Super League, a qualification round for 2023 World Cup in India.
Chasing 276, West Indies lost first-match century maker Shai Hope for just four in the first over to Shaheen Shah Afridi but Shamarh Brooks (42) and Kyle Mayers (33) added a brisk 67 for the second wicket.
Once Mayers, who hit four fours and two sixes off 25 balls, was bowled by pacer Mohammad Wasim, the innings fell away.
Nawaz dismissed Brandon King (nought), Brooks, Rovman Powell (10) and Nicholas Pooran (25) as West Indies lost five wickets for just 48 runs, including four off just 18.
Brooks hit four boundaries and a six as he faced 56 balls.
Nawaz’s previous best figures of 4-42 were against the same opponents in Sharjah six years ago.
Fast bowler Wasim finished with 3-34 while Shadab Khan took 2-40.
Pakistan won the first match by five wickets on Wednesday. The last match is on Sunday. All three are in Multan.
“I think we were 10-15 short because we lost back-to-back wickets,” said Azam.
“But there was spin so we were confident at the break that we could defend this and Nawaz took wickets at crucial junctures and brought us back in the game.”
Pooran praised Nawaz.
“It was a tough day for us,” said Pooran. “I thought we bowled well in the first 45 overs but conceded 20 too many. Credit must be given to Nawaz who bowled really well.”
Earlier, Azam, who on Wednesday became the first batter in ODI cricket to twice score three hundreds in as many matches, set the tempo after Pakistan won the toss and batted.
He built the innings during a 120-run second wicket stand with Haq -- their fourth successive 100 plus stand -- before Haq was run out, without watching his static partner while going for a single.
Haq hit six fours.
Pakistan were cruising along at 187-2 with Azam set for fourth hundred in as many ODIs when spinner Akeal Hosein dismissed the skipper in the 36th over.
Azam, who hit five fours and a six, failed to equal Sri Lanka’s Kumar Sangakkara’s record of four hundreds in as many ODIs set in the 2015 World Cup in Australia and New Zealand.
Azam’s wicket started a collapse as the West Indies grabbed five wickets in 23 balls for 20 runs, with Hosein (3-52) and Alzarri Joseph (2-33) sharing the spoils.
Fast bowler Anderson Phillip also chipped in with 2-50.
Joseph removed Mohammad Haris (six) and Shadab (22) while Hosein dismissed Mohammad Rizwan (15) and Nawaz (three).
Khushdil Shah (22), Wasim (17 not out) and Shaheen (15 not out) took the total past 250.