There was little by way of chances in the opening quarter of an hour until Georgios Kyriakopoulos flashed a low, deflected strike narrowly wide of the far post for the visitors.
At the other end, perhaps unsurprisingly for a team who had netted just one first-half strike in their previous seven outings, Patrick Vieira’s side were frustrated in their attempts to find a route to goal, seeing a handful of shots blocked and ultimately failing to test the goalkeeper.
They soon started to turn the screw though, and Andrea Pinamonti was twice denied by Stefano Turati.
He first pushed a towering header over the bar, before making a stunning stop low down to his right from a penalty, awarded after Kyriakopoulos manhandled Vasquez to the ground in the area.
Fabio Miretti then had an effort deflected inches over the bar as the White and Reds escaped to the break all square.
The onslaught continued in the second half, with Miretti, whose last goal came back in November, rattling the woodwork with a header, while Morten Thorsby was denied by Turati after making a lung-busting run from the centre circle.
The opening goal was surely just around the corner, and De Winter duly finally broke the deadlock in the 61st minute when - unmarked - he dived in to squeeze home a back post header from Aaron Martin’s deep free-kick.
That set Monza en route for an eighth defeat in their last nine outings, a run that means they remain seven points from safety at the foot of Serie A.
They had little by way of a response, whereas Genoa pushed for more, and after Miretti and Caleb Ekuban had wasted further chances, Vasquez wrapped up the points when making a well-timed run onto new signing Maxwel Cornet’s cross to power a header home.
The 2-0 scoreline means the Griffins, who were denied a third in injury time when De Winter had another header saved, have kept six clean sheets across their last nine outings, while the visitors have lost five successive away games for the first time since 2011 when they were in Serie C.
Flashscore Man of the Match: Johan Vasquez (Genoa)