After he was beaten by Parma in midweek, Juventus only needed 11 minutes to get their top-four bid here on the right track thanks to the unstoppable long-distance effort of Nicolas Gonzalez.
The Argentina International drove the field around the corner to drill a left shot along the vast Stefano Turati.
Not satisfied with their opener, Juventus threatened to add a fast second, while Randal Kolo Muani sent his shot wide from a promising one-on-one chance.
The Frenchman finally made up for that Miss when he was in a similar position just beyond the half -timepiece, calmly accompanying the ball in the far corner to score his first goal since the beginning of February.
Juventus seemed to enjoy the perfect first half, but they were reduced to 10 men in stopping time after a VAR review led to Kenan Yildiz being rejected for hitting Alessandro Bianco with his elbow.
The Bianconeri is perhaps left a man -light, but they still threatened to add to their advantage when González Turati forced a smart stop in the first 15 minutes of the second period.
Given their numerical advantage, it was not surprising to see Monza establish control over the ball in the second half, but they struggled to translate their considerable possession into clear opportunities, perhaps show why they are the second lowest scorers in the competition.
Gianluca Caprari eventually forced Michele di Gregorio into action in the dying sintels of the game, but in reality his weak header did not offer much threat to the Juventus Shot stopper, who helped the club claim their 16th beautiful laymen from the Serie A-season.
While the side of Igor Tudor increased their hope at the UEFA Champions League, Monza remains stranded at the bottom of the table after their 12th defeat in 14 league matches, which means they run the risk of being banished at the end of the day.
Flash score Man of the match: Nicolas Gonzalez (Juventus)
View all match statistics with flash score.