The decisive moment in the match came early in the second period when Leverkusen's Victor Boniface showed his striker's instinct to follow in an effort at goal and emphatically hand Xabi Alonso's side the three points.

Leverkusen, beaten Europa League finalists in May, have continued their excellent form from last season, winning both of their matches in Europe's top club competition with five goals scored and zero conceded.

But it was a second defeat in two Champions League outings for seven-times winners Milan after they lost 3-1 at home to Liverpool in matchday one.

"It's true that we didn't win, but it was the performance I liked the most since my arrival here," AC Milan coach Paulo Fonseca said to Sky Sport Italia.

"Especially in the second half, we had a fantastic performance. We created so many chances and just failed to convert them, which is not easy against a team like Bayer."

Boniface thought he had given the German champions the breakthrough in the 21st minute, only for VAR to deny him a first goal in the Champions League proper for an offside in the build-up.

The hosts continued to push as they got the upper hand on their Italian opponents.

German starlet Florian Wirtz was at the heart of everything Leverkusen created and Boniface was a continual thorn for the defence.

Mike Maignan in the AC Milan goal kept the encounter goalless going into the second half.

Leverkusen dominance finally paid six minutes after the interval when Boniface smashed home from close range after Maignan could only parry a low near-post drive by Jeremie Frimpong across the goal-line to the waiting Nigerian.

The goal sparked some life into the Italians. They started to pose a threat, with Youssouf Fofana hitting two strikes from distance that had goalkeeper Lukas Hradecky interested.

Frimpong had an excellent chance on the counter to seal the game with 15 minutes remaining but his finish lacked composure and he only found the side netting with just Maignan to beat.

The visitors came within inches of grabbing an equaliser inside the last 10 minutes when Theo Hernandez's deflected shot bounced over Hradecky and onto the bar. Then Alvaro Morata's headed rebound went agonisingly wide of the far post.

Hradecky then was forced to fist away a rasping Ruben Loftus-Cheek strike on the half-turn.

Leverkusen still posed a threat going forward and came within a whisker of wrapping up the match in injury time with a left-footed shot from Nathan Tella that flashed narrowly past the far post.