MUNICH - Bayern Munich cruised into the quarterfinals of the Champions League after a 7-0 win over Shakhtar Donetsk with the visitors losing a defender to the fastest red card in the competition's history.

Thomas Mueller notched two goals, while Jerome Boateng, Franck Ribery, Holger Badstuber, Robert Lewandowski and Mario Goetze added one apiece as the German champions matched its biggest home win.

Olexandr Kucher was sent off in the third minute for tripping Goetze, who was racing toward goal.

"The red card was decisive but we played a very good match as well," Bayern midfielder Bastian Schweinsteiger said.

Mueller converted from the penalty spot in the fourth minute to get Bayern going with the opening goal of the tie after a goalless first leg in Ukraine.

Boateng added the second in the 34th as Shakhtar struggled in all departments.

Ribery and Mueller scored early in the second half with Lewandowski and Goetze getting on the scoresheet late on.

Bayern, a five-time champion, also beat Basel 7-0 in the same Round of 16 stage in 2012.

Shakhtar failed to make a shot on target in the entire match.

"I feel sad that we lost with such a result," Shakhtar's coach Mircea Lucescu said. "After the third goal the match was over."

Bayern coach Pep Guardiola said it was the first time he started "such an important match" with five forwards and was pleased with the outcome.

"We controlled the flanks very well, perfectly. With one man up, it was a little simpler," Guardiola said.

Arjen Robben went off in the 19th with an injury and Ribery also hobbled off in the 60th. Guardiola said the injuries did not appear serious.

Boateng scored after Lewandowski's attempt was blocked and the defender was alone at the far post to drill the ball into the roof of the net.

Ribery was felled by Douglas Costa away from the ball but got away with only a yellow card.

Ribery made it 3-0 in the 49th, taking a pass from Boateng, cutting in from the left and firing into the far corner.

Mueller got his second in the 52nd, following Ribery's delivery from the line.

With Bayern cruising, it only became a matter of how many goals the German champion would score.

Badstuber headed home with an unchallenged header in the 63rd and Lewandowski raised the score in the 75th after picking up a long through pass from Schweinsteiger.

"The red card and the penalty really played into our hands and then we controlled the match until the end," said Badstuber, who played his first Champions League match in two years following a knee injury.

Goetze completed the scoring in the 87th after good work by Boateng.

Victory sees Bayern advance to its fourth consecutive quarterfinal. It is also the first club to make it to 14 quarterfinals overall.

In the other match, 10-man Paris Saint-Germain advanced on away goals after earning a 2-2 draw at Chelsea to draw 3-3 on aggregate.