Goals in the last nine minutes from Peruvian international Claudio Pizarro and Lucas Podolski secured Bayern's second win in as many Group B matches and left Inter still looking for their first point.

The Serie A leaders also had Zlatan Ibrahimovic and Italy international Fabio Grosso sent off as they crashed to their second successive defeat, leaving them with a mountain to climb to reach the last 16.

Ibrahimovic trudged off near the hour mark after picking up a second yellow card and Pizarro broke the deadlock nine minutes from time with a cool finish.

Grosso joined the Swede for an early bath before a swift breakaway goal by Bayern substitute Podolski sealed Bayern's first win away to Italian opponents in European competition since the 1988-89 season.

The win meanwhile ends Bayern's Italian jinx as they scored their first win in seven matches against opposition in Italy.

Inter sorely missed the grit and determination of their French midfielder Patrick Vieira, whose sending-off against Sporting Lisbon two weeks ago earned him a one-match ban.

Despite back-to-back losses in Europe, Inter Milan coach Roberto Mancini insisted his team would still qualify from the group.

"The defeat this evening was a lie," he said defiantly.

"We were controlling the match until Ibrahimovic was sent off and the first goal could have been avoided.

"But there are four games left to play in the group and we will qualify in second place."

Bayern coach Felix Magath agreed with Mancini that Ibrahimovic's dismissal swung the match in his favour.

"That was the turning point," he said. "After we took the lead, Inter were chasing the game and that allowed us to snatch a second goal.

Magath said the victory did not taste any sweeter given the poor record they had against Italian clubs away from home.

"We don't look at statistics," he said dryly.

Wednesday's match at the San Siro saw the captains of both teams reach significant landmarks.

Inter's Argentine midfielder Javier Zanetti played in his 500th match for the club, while German international goalkeeper Oliver Kahn made his 100th Champions League appearance for Bayern.

Kahn, Bayern's hero when they won the 2001 Champions League on penalties against Valencia, came to his side's rescue in the 12th minute.

Inter's Serbian midfielder Dejan Stankovic stole possession from Pizarro before sweeping the ball wide to the left wing where Ibrahimovic was prowling.

The giant Swedish international sped towards goal but allowed the ball to run too far ahead of him, and his feeble shot was blocked by the Bayern skipper.

Kahn's counterpart Julio Cesar saved Inter from falling behind in the 22nd minute.

Dutch striker Roy Makaay escaped his marker and fired an angled shot that was heading for the corner of the net, but the Brazilian keeper's outstretched leg kept the hosts on level terms.

Inter, whose biggest problem was containing the incisive runs of German international Philipp Lahm, one of the stars of this year's World Cup, finished the first half on top with Grosso and Ibrahimovic both firing narrowly wide.

Bayern started the second half brightly with Pizarro's head an inch away from applying the finishing touch to Lahm's left-wing cross.

Marco Materazzi was lucky to stay on the pitch after his wild tackle stopped Bayern's Brazilian defender Lucio in his tracks, before Mark van Bommel curled a shot inches past the post for the visitors.

Ibrahimovic saw red for a second yellow in the 58th minute before Kahn denied Hernan Crespo with a breathtaking one-handed save.

Pizarro finally made the breakthrough in the 81st minute, clipping the ball past Julio Cesar after sneaking in unmarked behind the Inter defence to latch onto Roy Makaay's chipped pass.

Grosso received a straight red card somewhat harshly for using an elbow on Bastian Schweinsteiger in the final minute before Podolski netted his first goal for Bayern since his summer move from FC Cologne.

The 21-year-old striker raced clear after an attempted back pass by Ivan Cordoba fell short before walking round Julio Cesar and slotting home.