Bayer Leverkusen’s Victor Boniface scored a second-half goal to secure a 1-0 home win over AC Milan in the Champions League on Tuesday. This means the German team has a perfect start to the season, while the Italians still don’t have a point.

Bundesliga champions Leverkusen have six points after beating Feyenoord 4-0 in their opening game, while Milan lost 3-1 at home to Liverpool in the competition’s first game.

The only goal at the BayArena came six minutes after the break when Boniface fired home a rebound after Milan keeper Mike Maignan parried a shot from Jeremie Frimpong.

“I think it’s great news that German football is competitive. It is also good news for us that we achieved this result against Milan,” said Leverkusen coach Xabi Alonso after the game. “Our first 60 minutes were good, but in the end we suffered from fatigue after the game against Bayern Munich.

“We showed spirit and character, these three points are very good. In the Champions League you have to be able to suffer and fight, not just play well.”

It was no more than the home side deserved after a first half in which they had the majority of possession and most of the chances but could not find a way past Maignan as Milan struggled to gain a foothold in the game.

The goal spurred the visitors into action and they threatened to equalize as they held Leverkusen back for much of the second half, but they suffered their second defeat in the first two games of the competition.

Leverkusen had two early chances in the opening minutes when Maignan Boniface parried and then parried Piero Hincapié’s header in the following corner.

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The hosts surged forward at every opportunity and thought they had found a way to get through when Boniface had the ball in the net, but Frimpong was offside as he collected a pass down the wing to send in the cross.

Maignan kept Milan in the game by making saves from Alex Grimaldo and Florian Wirtz, with Frimpong wasting chances on the rebound in both cases, but Boniface made no mistake when his chance came.

Grimaldo’s backheel pass set up Frimpong for the shot, which Maignan was able to reach again, but Boniface had the easiest chances from close range and Leverkusen were in the lead.

Milan coach Paulo Fonseca said before kick-off that he did not want to risk Álvaro Morata from the start, but with his team hoping for an equalizer, the Spanish striker was substituted on for Tammy Abraham in the 62nd minute.

Morata had the chance to make his effort count when Theo Hernández’s long-range shot deflected off the crossbar. Morata hit the rebound, but his header went wide of the far post.

In the final minutes, Leverkusen defender Hincapie attacked Ruben Loftus-Cheek on the edge of the penalty area, which the Milan coach believed should have resulted in a penalty.

“For me it’s a penalty, it’s an interference on the line,” Fonseca said. “The strange thing is that they haven’t even checked the situation yet. The referee had no doubts during the game, but I don’t like to talk about the referee.”

Milan had another late chance to equalize, but Leverkusen’s Lukas Hradecky parried a shot from Loftus-Cheek on the turn and the home team held on to secure all three points.