With head coach Massimiliano Allegri not on the bench through suspension, the Bianconeri put in a poor display as Di Maria was sent off for an elbow on Armando Izzo before half-time.
The visitors’ sloppy performance was punished 16 minutes from time as Gytkjaer slammed home from a Patrick Ciurria’s cross.
A first league defeat of the season for Allegri’s men means they lose more ground on Serie A’s early pace-setters, adding to the scrutiny of the coach.
Monza started brightly with Nicolo Rovella, on loan from Juventus, flashing a volley wide of the left post.
Izzo missed a great chance to break the early deadlock as he headed over from a Marlon Santos cross, before Patrick Ciurria’s side-footed effort was just off the mark.
Juventus struggled to get going, with Dusan Vlahovic finally registering their first shot on target in the 28th minute with a tame attempt that was easily saved.
The Bianconeri were down to 10 men before the break, as Di Maria saw red for a petulant elbow in the chest of Izzo as the two battled for possession.
After the interval, the home side’s Dany Mota should have done better when he turned a cross past the post, before Juventus goalkeeper Mattia Perin made a smart stop to keep out Carlos Augusto’s powerful shot.
The hosts finally got their reward when Gytkjaer smashed home from Ciurria’s deflected cross to spark wild celebrations from the home faithful.
Juventus pushed for an equaliser, but an easily saved Moise Kean header was as close as they came, making it now five games without a victory in all competitions for the Turin giants.
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