Having dominated the opening five minutes, Monza’s defensive frailties were laid bare in Udinese’s first attack when Jordan Zemura picked out Lorenzo Lucca, who rose to meet the cross from the left, burying a header for his first goal since the end of October.
Lucca then thought he had two in three minutes, finishing high into the roof of the net having been played through by his captain Florian Thauvin, yet his celebrations were cut short by the offside flag.
To their credit, Alessandro Nesta’s strugglers fought back and it seemed as though Alessandro Bianco was doing some shooting practice as he fired no fewer than three shots wide from the edge of the box.
At the other end, Thauvin perhaps should have been selfish when he was at the byline but attempted a cutback that found nobody in black and white.
The first half ended with the Biancorossi on top again, with Pedro Pereira and Warren Bondo coming close as the visitors held their lead at the break.
The hosts were probably disappointed to hear the half-time whistle but kept their foot on the gas after the break and were level just two minutes in.
After Daniel Maldini went on a barrelling run into the box, taking three Udinese defenders with him, the ball dropped to Georgios Kyriakopoulos, and the Greek international buried a low first-time finish past debutant goalkeeper Razvan Sava.
The pressure continued thereafter, with Gianluca Caprari dragging an effort wide and Sava denying a Milan Duric header.
The game fell into a lull after this as Monza’s momentum faded and they were made to pay on 70 minutes through an unlikely source.
Kosta Runjaic’s men broke at pace and Jurgen Ekkelenkamp played in the surging centre-back Jaka Bijol, who showed the composure of a striker to finish between the legs of Stefano Turati.
There were heads in hands around the Stadio Briantero eight minutes later when substitute Dany Mota crashed a header against the crossbar.
That was as close as under-pressure Nesta’s men came to an equaliser as they remain 19th, only ahead of Venezia. Udinese, meanwhile, are propelled into the top half of the table in ninth.