Mario Gomez scored a first-half hat trick

Mario Gomez scored a first-half hat trick as Bayern Munich took a major step toward the knockout stage of the Champions League by defeating Napoli 3-2 on Wednesday.

Gomez opened the scoring in the 17th, taking advantage of an opening in Napoli’s defense. Bastian Schweinsteiger saw the space and sent a through ball to Gomez, who shook off Hugo Campagnaro and slotted past goalkeeper Morgan De Sanctis.

It was Bayern’s 250th goal in the Champions League. Gomez doubled the lead in the 23rd, when Toni Kroos floated a perfect cross behind Napoli’s defense to the unmarked striker. Gomez easily drove the ball past De Sanctis.

In the 42nd, Bayern produced one of the best moves of the match, with Franck Ribery feeding Kroos as the Napoli defense stood helplessly. De Sanctis stopped Kroos’ effort but couldn’t hold onto the ball and Gomez tapped in from close range.

Gomez now has 13 goals in his last 10 Champions League games. With a total of 17, he is the top German scorer in the competition. “We wanted to be aggressive but we knew that they also would be aggressive,” Gomez said. “We allowed a couple of counterattacks in the first half but otherwise did very well before the break.

Naples Italian head coach Walter Mazzarri throws a bottle in the Allianz Arena

• Schweinsteiger out until New Year

Bayern Munich and Germany midfielder Bastian Schweinsteiger has undergone surgery on his broken collar bone and will be out of action until the New Year, the Bavarian club said on Thursday.

"The fracture was successfully repaired and a plate inserted in an operation performed at around 2 a.m. on Thursday morning," said Bayern, after the player was injured during Wednesday's 3-2 win over Napoli in the Champions League. Bayern said Schweinsteiger will stay in hospital until Friday and must rest completely for two weeks after that.

"The first step in his sports rehabilitation programme will be to resume jogging, before the player is cleared to resume training with the team in approximately six weeks.

"That in turn means Schweinsteiger will not play again this calendar year," it added.

"It's a blow, because he's been in outstanding form recently," said coach Jupp Heynckes. "In the second half, we saw how important Bastian is to the team. Our game suffered badly after he went off."