Milan have now picked up 22 points after eight league games, their best record in the three-points-for-a-win era, going back to 1994-95.
“Verona were better than us in the first half, we were unlucky with the first goal but reacted after the break," Milan coach Stefano Pioli told Sky Italia.
“I saw the right expressions on the faces of the players at halftime, we had to step it up and we did. It was a great test of maturity."
A Gianluca Caprari strike and Antonin Barak penalty gave the visitors a comfortable halftime lead, but Olivier Giroud halved the deficit with a 59th-minute header.
The Rossoneri then turned the game on its head in the space of two minutes, as Franck Kessie equalised from the penalty spot and Koray Gunter steered an attempted clearance into his own net.
There was further good news for the hosts when Zlatan Ibrahimovic, their top scorer last season, made his return from injury from the bench for the final 13 minutes after more than a month out.
"Everyone knows his presence is very important to us. He is not yet in top condition, I hope he can improve and play a lot of games," Pioli said.
Milan are one point clear on top ahead of Napoli, who play Torino on Sunday, while Verona are 13th with eight points.
Pioli’s side had a bad week with injuries, as goalkeeper Mike Maignan was ruled out for 10 weeks following wrist surgery before Theo Hernandez and Brahim Diaz tested positive for COVID-19.
They looked like a depleted force in the first half as stand-in keeper Ciprian Tatarusanu was forced into a save on an Ivan Ilic shot before Caprari smashed in the opening goal after seven minutes.
Things got worse when Barak converted a penalty after Nikola Kalinic went down under a challenge from Alessio Romagnoli, and Milan’s injury list grew longer when Ante Rebic limped off.
But the hosts were a team transformed in the second half and pulled one back when Giroud, making his first appearance since the end of September due to injury, headed in a Rafael Leao cross.
Kessie pulled Milan level with a 76th-minute spot-kick, and two minutes later Gunter had a moment he will want to forget quickly when a cross came in and he could not sort his feet out and accidentally guided a volley into his own net.
Ibrahimovic’s return gave the home crowd another moment to cheer, and the Swede tried to make it a memorable comeback with a spectacular overhead kick attempt, but he did not connect properly.