Thomas Muller scored twice as Bayern Munich put in their best pre-season performance so far in a 3-2 victory over Chelsea in Singapore.

Carlo Ancelotti's side lost on penalties to Arsenal and then 4-0 to AC Milan in their previous International Champions Cup fixtures, and concerns had begun to surface about their ability to cope with the retirement of influential stars Philipp Lahm and Xabi Alonso at the end of last season.

Brazilian full-back Rafinha soothed those worries by scoring an opening goal that had all the hallmarks of Lahm's attacking game, before Muller scored with two fine strikes as the Premier League champions were overrun by their Bundesliga counterparts.

Marcos Alonso pulled one back for the Blues shortly before half-time, and Antonio Conte introduced star signing Alvaro Morata for his first pre-season appearance in the second half.

Morata had a hand in Michy Batshuayi's late consolation goal in a second half that saw Bayern continue to create the better of the chances, many of which fell to the Spain striker's former Real Madrid team-mate James Rodriguez, who endured a frustrating evening.

Bayern, keen to make amends for a disappointing performance in their drubbing by Milan, started the game brightly with veteran winger Franck Ribery probing forward down the left flank.

It was a cross-field pass from Ribery that allowed Rafinha to break down the right and hit a low, bouncing shot across the face of goal that found the net via Thibaut Courtois' right-hand post.

Ribery was again the architect when Bayern made it 2-0 after 11 minutes, skipping into the box and cutting the ball back into the path of the onrushing Muller, who volleyed home from close range.

Muller scored the pick of the goals after 26 minutes after he was put through by Corentin Tolisso and then allowed to run at Chelsea's defenders, who backed away while the Germany international curled a powerful 25-yard shot beyond Courtois and into the top-right corner.

Chelsea improved before half-time and enjoyed a spell of pressure that culminated in Alonso pulling a goal back, arrowing the ball across Tom Starke and in after Victor Moses' low cross found him unmarked on the left side of the penalty area.

Marco Friedl's superb curling cross after 56 minutes found the head of James, who was only inches away from the target with his attempt, and the Colombian star was denied from by a last-ditch Gary Cahill challenge as he bore down on goal four minutes later.

Conte sent on Morata along with David Luiz after 63 minutes but Chelsea were frequently stretched throughout the last half hour of play and James should have done better when Ribery teed him up for a shot from 15 yards that he dragged wide.

David Luiz saw a deflected effort hit the post, before Chelsea set up a frantic finish when Morata flicked Cesc Fabregas' corner into the path of Batshuayi to bury, but it was too late to alter the result.