Reports suggested that Filippo Inzaghi would be dismissed as Milan manager if they failed to win tonight, and a draw may not be good enough to keep him in employment.
Menez appealed for a penalty in the sixth minute, but was denied by the referee. He then took a powerful shot from long range, which hammered against Emil Hallfredsson, leaving the Verona player on the floor.
Verona threatened the Milan goal in the 12th minute. A counter-attack was played towards Jacopo Sala, whose shot from the right side of the penalty area went narrowly wide of the net.
Mexes's shot was saved by Francesco Benussi after 25 minutes and Menez forced another save a few minutes later as Milan replied with promise.
It was Mexes to threaten again on the half-hour mark when a shot from 40 yards looked destined for the top right corner only to go narrowly wide.
Defender Mexes was in the thick of things offensively and won his team a penalty in the 40th minute. Menez stepped up to power the ball into the middle of the net.
The French centre-back grabbed a goal from the restart. The Verona defence failed to deal with Menez, who found Mexes inside the area and he rounded Benussi and squeezed the ball in from a tight angle.
Milan grew in confidence at the start of the second half. Giampaolo Pazzini forced a save from Benussi before a 24-pass move was deflected for a corner a few minutes later.
That did not last for long, however, as the hosts sat back. Toni failed to hit the target on two occasions and Sala shot wide following a skilful dribble into the area.
Panagiotis Tachtsidis nearly scored from 30 yards out. His effort beat Lopez, but deflected off the crossbar and away.
Verona continued to dominate the latter stages and substitute Nicolas Lopez breached the Milan defence on 94 minutes to secure a point for his team.