Coach Louis van Gaal admitted he was a relieved man after Bastian Schweinsteiger netted twice as Bayern Munich fought back to seal a 2-1 win at Basel in the Champions League.

Bayern Munich's Bastian Schweinsteiger celebrates his winning goal against Basel Wednesday. Photo: AFP

Basel took an early lead when striker Marco Streller held off Bayern defender Holger Badstuber in the penalty area before back-heeling his pass into the path of Swiss star Alexander Frei who fired home after 18 minutes.

Bayern bounced back as Schweinsteiger kept his cool to net a second-half penalty before giving his side their second win in Group E with an 89th-minute goal to save the Germans' blushes.

"I am very relieved, we fought hard for the victory," said van Gaal.

"I am pleased we came back from 1-0 down. It was a bit unlucky that Basel scored the first time they got over the halfway line and with their first shot."

"We lost a bit of confidence and we played badly in the first half, but we turned things around."

Bayern captain Mark van Bommel said he had read his side the riot act at half-time after a poor first-half display.

"After we went 1-0 down, we had to defend hard until half time," he said.

"I was very loud in the dressing room, as was our goalkeeper, and van Gaal pretty much agreed with both of us. We had the game under control after the penalty."

"It is very important we won, six points is a good start."

Bayern are at Dortmund on Sunday in the Bundesliga and van Bommel says his side needs a win to keep the German press off their backs after last Saturday's 2-1 shock defeat at home to new league leaders Mainz.

"If we don't win in Dortmund this weekend, the next few weeks are going to be made difficult for me," admitted the Dutchman."

Basel coach Thorsten Fink, a former Bayern Munich player, said he was disappointed to lose so late in the game.

"That was a typical Bayern Munich goal by Schweinsteiger in the 89th minute," said Fink.

"I am disappointed we lost just before the final whistle. There was a huge difference in class: Bayern's squad is worth 300 million euros (US$408 million) compared to our 30 million in market value, but we have a good team.

"We leave the stadium with our heads held up high and we played well."

"For the rest of the Champions League, we are not totally without a chance of second place and a place in the Europa League is realistic."

In the next round of matches, Bayern host Romanian side CFR Cluj in Munich on October 20, the same night Basel are at Roma in Group E.