A stunning stoppage-time strike by Frans Kratzig sealed victory for Bayern Munich in a pre-season friendly against Liverpool in Singapore on Wednesday as the German league champions came from behind twice to win 4-3.

The 20-year-old fired past Alisson as the game entered stoppage time to settle a thrilling encounter in front of a crowd of nearly 50 000 fans at the National Stadium.

A goal inside two minutes by Cody Gakpo and a header by Virgil van Dijk had put the English side two goals up in the opening half-hour but Bayern hit back through Serge Gnabry and Leroy Sane to level the score before halftime.

Luis Diaz regained the lead for Liverpool midway through the second half before Josip Stanisic drew level at 3-3 in the 80th minute and Kratzig secured the win for Bayern at the death.

Liverpool had trounced Leicester City 4-0 at the same venue last Sunday and they caught the German champions napping with their opening goal after 112 seconds.

Gakpo played a neat one-two with Diogo Jota on the halfway line and surged past the Bayern defence before firing past Yann Sommer into the roof of the net.

Bayern should have equalised in the 10th minute but Benjamin Pavard headed against the woodwork from five metres out before nodding the rebound over the crossbar.

They would rue that miss when Liverpool extended their lead in the 28th minute through newly appointed captain Van Dijk who rose unchallenged in the Bayern box to head in Andy Robertson's corner from the right.

Bayern reduced the deficit five minutes later as Kim Min-jae's ball over the top of the Liverpool defence found Gnabry who cut inside Joel Matip before slotting past goalkeeper Alisson with his right foot.

Gnarby also played a big part in Bayern's equaliser three minutes before halftime.

Sent clear down the left flank by Mathys Tel, the German international winger surged into the Liverpool box before squaring the ball for an unmarked Sane to fire home with his left foot.

Halftime substitute Darwin Nunez should have restored Liverpool's lead early in the second half when he headed wide with the goal at his mercy.

At the other end, Jamal Musiala had his attempt from point-blank range blocked by an alert Alisson.

But the English side would go back in front in the 66th minute after some fine work by Mohamed Salah who cut in from the right flank before feeding the ball to Diaz for an emphatic finish.

With 10 minutes remaining, Bayern hit back.

Alisson made a fine reflex save to keep out Kratzig's powerful header but the rebound went to Stanisic who turned the ball in from close range.

Nunez then squandered another chance to get a fourth for Liverpool after he was played in by Diaz.

Kratzig made them pay for the miss when he gathered a long ball from Matthijs De Ligt with an excellent first touch before rifling an unstoppable effort past Alisson.