Zucker, who was acquired from the Minnesota Wild in a trade on Monday, scored both goals in the final two minutes of the second period to give the Penguins a 3-1 lead.
Sidney Crosby had three assists, Kris Letang and Zach Aston-Reese also scored, and Tristan Jarry made 34 saves for Pittsburgh, which moved back within three points of the Washington Capitals for first place in the Metropolitan Division.
The Penguins are 10-3-1 in their past 14 games. Pittsburgh, which lost 2-1 in overtime to the visiting Tampa Bay Lightning on Tuesday, hasn't dropped two in a row since Nov. 29-20. Zucker made his Penguins debut against the Lightning and didn't record a point.
Brendan Gallagher scored, and Carey Price made 24 saves for Montreal, which has lost three in a row following a 9-3-0 stretch.
After a scoreless first period, the teams combined for four goals in the second, including three in the final two minutes.
Ilya Kovalchuk was in the penalty box for slashing Zucker when the Penguins took a 1-0 lead at 7:25.
As the penalty winded down, the puck was trapped in the corner of the Montreal zone when Penguins forward Patric Hornqvist dug it out and passed to Crosby above the left circle.
Crosby quickly sent the puck to Letang in the right circle, and Letang had room to skate to the dot and blast a wrist shot high into the net.
Crosby set up Zucker for a one-timer to make it 2-0 with two minutes left in the second period.
Gallagher made it 2-1 with a power-play goal with 54 seconds left in the middle period. However, Zucker re-established a two-goal lead with 18 seconds left before the second intermission, redirecting a centering pass from Marcus Pettersson.
Crosby's third assist of the night gave him 17 points (five goals, 12 assists) in 11 games since returning from core muscle surgery.
Aston-Reese scored into an empty net with 1:44 left to make it 4-1.
--Field Level Media