Mujeeb grabbed four wickets in five deliveries spread across two different overs - and spells - to wreck West Indies' pursuit of 190, and their downfall was swift thereafter. They were eventually bowled out for 150.
Before Mujeeb's 4 for 21, Rasooli and Atal enjoyed a 115-run third-wicket stand to hold Afghanistan's batting innings together. A late cameo from Azmatullah Omarzai on a turning surface made the total even more daunting.
The win made it a hat-trick of T20I series wins for Afghanistan. The two teams meet again on Thursday for what will be Afghanistan's final T20I before the T20 World Cup. West Indies will seek a consolation win before their tour of South Africa.
Mujeeb runs through West Indies
West Indies' chase started poorly. They lost newly promoted opener Alick Athanaze to a direct hit in the third over, and they could score only 29 in the powerplay, squeezed by Fazalhaq Farooqi's opening spell.
Mujeeb, who bowled two overs in the powerplay, then returned in the eighth and went around the wicket to skid one straight through and hit No. 3 Evin Lewis' pad before he could bring out a shot.
When right-hander Johnson Charles walked in next, Mujeeb came over the stumps and got a delivery to drift in beautifully from outside off and through the gate to peg back off stump as the batter drove away from his body. West Indies were 38 for 3.
But they were not going down without a fight, and Shimron Hetmyer's assault on Rashid Khan and Noor Ahmad kept West Indies in the game. Hetmyer pumped six sixes in a 17-ball 46. Farooqi, however, dismissed him in the 14th over, and Rashid brought Mujeeb back for his third, with West Indies needing 68 runs in five overs.
Mujeeb kept his length back, and with West Indies desperate for big shots, Brandon King (50) came down the track and miscued the hat-trick ball down to long on. Mujeeb wheeled away in celebration, having become the third Afghanistan bowler to achieve the feat after Rashid and Karim Janat. Two balls later, T20I newbie Quentin Sampson failed to put bat on a googly, and Mujeeb had his fourth.
The lower order offered little resistance, as West Indies lost their last five wickets for 27 runs.
Rasooli doubles down in Atal's company
On Monday, Rasooli had smashed 84 in a 162-run stand with Ibrahim Zadran to set up Afghanistan's series-opening win, and on Wednesday he combined just as effectively with Atal.
As in the first game, Afghanistan lost both openers inside the powerplay, and Rasooli ensured there were no stutters by taking the aggressive route with his square cuts, drives through the off side and flat-batted shots down the ground.
Helped by let-offs from the West Indies fielders, Rasooli reached his fifty in 22 balls - his third in a row for Afghanistan - while Atal was more watchful.
Rasooli powered along through the middle overs, taking down Khary Pierre and Gudakesh Motie. Atal and Rasooli fell in the 17th and 18th overs respectively, but with the big-hitting Mohammad Nabi and Omarzai walking in next, there was no respite for West Indies. Motie, left to bowl the 20th over, conceded 19 with Omarzai hitting him for back-to-back sixes, and Afghanistan posted 189 for 4.