Luis Diaz and Harry Kane scored the goals that gave dominant Bayern Munich a crucial 2-1 UEFA Champions League quarter-final first leg win away to Real Madrid on Tuesday.

Kylian Mbappe's strike 16 minutes from time gave record 15-time winners Real a lifeline at their Bernabeu home in a gripping battle.

Vincent Kompany's side, arguably the strongest team in Europe this season, produced a masterclass in the first half and could have been several goals ahead. Instead they had only one from Diaz, which Kane added to after the interval, but French superstar Mbappe's goal kept Alvaro Arbeloa's side in the tie.

"It's a shame it wasn't 2-0 at the end to be completely honest," said Bayern goalkeeper Manuel Neuer, who made several good saves in the second half as Madrid ramped up the pressure. 

"You know how dangerous Real Madrid are, we saw that again today. They had plenty of chances and could've scored more. First up we're happy about the victory here away from home, but it'll be a tough challenge back in Munich."

Real Madrid defender Antonio Rudiger said that Mbappe's goal had kept the tie open. "For me, the two goals we conceded were gifts, and in the second half we needed more," Rudiger told Movistar. "I think we're alive, everything is open with that goal from Mbappe. I think we had many chances to score goals, but in the end this is how it is."

In Lisbon, Kai Havertz snatched a last-gasp winner as Arsenal bounced back from their domestic distress to steal a 1-0 victory at Sporting CP in the Champions League quarter-final first leg on Tuesday.

Mikel Arteta's side arrived at the Jose Alvalade Stadium rocked by successive defeats against Manchester City in the League Cup final and Southampton in the FA Cup quarter-finals.

Once again, the Gunners were below their best but they emerged with the win thanks to David Raya's fine saves and Havertz's clinical finish in stoppage-time.

Arsenal will be firm favourites to advance to the semi-finals in the second leg in north London on April 15, but they will have to improve significantly to win the tournament for the first time.

Those agonising losses to City and second-tier Southampton marked the first time that Arsenal had been beaten in successive matches this term, with the embarrassing FA Cup defeat just the Gunners' fifth of the season.

The after-shocks were still being felt as Arsenal struggled to find any momentum in Lisbon, but not for the first time this season they found a way to win ugly.

"We had to be a little bit crisper, faster, more efficient to break them down when they had that block," Arteta said.

"We had a goal disallowed and there were two or three occasions where we were close but we lacked that final pass. In the end a magic moment from the finishers win us the game.

"It's beautiful and that's the impact you need when you get to this stage of the season. Everybody has to make an impact and they certainly did that tonight."