The Uruguayan forward repeated his feat from earlier this season, when he came off the bench to rescue a point against Inter at San Siro with a late goal to seal a 2-2 draw back in November.
That equaliser came in the 89th minute and this one was even later as he struck in the final minute of five added on to the end of the second period to deny the hosts.
Verona had earlier taken the lead through Luca Toni's penalty, but Milan hit back either side of half-time to move in front.
Philippe Mexes - returning to the side after a four-week ban for grabbing Lazio's Stefano Mauri by the throat - won a penalty that was converted by Jeremy Menez.
Mexes then had a crucial hand in the goal that put Milan 2-1 up and it looked to have sealed a much-needed triumph for the under-pressure Filippo Inzaghi, who had rejected rumours this week that assistant Mauro Tassotti was set to take his place as Milan coach.
However, it was not to be for Milan and Inzaghi, as Lopez ran onto Toni's flick and slotted the ball home to spark scenes of wild celebration among the visiting staff and players, who had earlier seen coach Andrea Mandorlini sent off for protesting against a decision.
After a quiet opening to the game, Verona's Jacopo Sala had the first sight of goal when he flashed a shot narrowly wide of the left-hand post in the 12th minute.
Six minutes later, Verona were in front through Toni's cheeky spot-kick.
Sulley Muntari clumsily felled Artur Ionita inside the box and the veteran striker calmly sent a chipped effort straight down the middle of the goal.
Verona continued to look the more threatening side and went close to a second when Ionita was denied by the legs of Diego Lopez on the half-hour mark.
Somewhat against the run of play, Milan drew level through a penalty of their own four minutes prior to the interval.
Mexes went down under a challenge from Bosko Jankovic and Menez thumped home the resulting kick.
Milan made a positive start to the second period and were ahead within two minutes as Mexes' effort from an acute angle struck Eros Pisano and then Panagiotis Tachtsidis on the line before creeping into the net.
Verona came agonisingly close to an equaliser 17 minutes from time when Tachtsidis' rasping volley struck the underside of the crossbar before bouncing down and away to safety.
Just when it seemed Milan would hold on for only their third league win in 11, Lopez struck to heap further pressure on Inzaghi.
