Nicolas Gonzalez scored the opening goal after just 11 minutes, driving across the pitch to create space and drilling a left-footed shot past the outstretched goalkeeper Stefano Turati.
Juventus continued to press for a second goal, with Randal Kolo Muani coming close with a shot that went wide from a one-on-one opportunity.
Muani made amends for his earlier miss when he scored his first goal since February, calmly guiding the ball into the far corner just past the half-hour mark.
Juventus was reduced to 10 men in stoppage time after Kenan Yildiz was sent off for striking Alessandro Bianco with his elbow, but they continued to threaten Monza's goal.
Monza had more possession in the second half, but struggled to create clear-cut chances, reflecting their position as the second-lowest scorers in the league.
Gianluca Caprari's weak header in the dying minutes was the closest Monza came to scoring, but Juventus goalkeeper Michele Di Gregorio was not tested.
Juventus' win boosted their UEFA Champions League hopes, while Monza remain at risk of relegation after their 12th defeat in 14 league games.
Juventus' Nicolas Gonzalez was the standout player, earning the Man of the Match award.