Bayern have the advantage heading into the second leg of the quarter-finals. Arsenal are in the same position.
But the 1-0 victory against Sporting was a long way off. It wasn't until the first minute of added time that substitute Kai Havertz scored the winner.
At the Santiago Bernabéu in Madrid, Luis Díaz scored Bayern's opening goal with a few minutes left in the first half. The set-up was provided by Michael Olise and Harry Kane.
Shortly after the break, Bayern created an excellent opportunity ahead of the return leg on Tuesday in Munich. Olise played Kane in and he made it 2-0.
Kane's eleventh goal
Kane is now up to eleven goals in the Champions League this season.
But a goal by Kylian Mbappé reduced the deficit and gave the "Meringues" hope.
The Iberian Peninsula was the scene of tonight's quarter-finals.
In Lisbon, Arsenal's Viktor Gyökeres received a warm welcome upon his return to the José Alvalade stadium, where he scored for Sporting. He was applauded by the stands as he touched the pitch ahead of the match.
The Swedish national team striker smiled and showed his appreciation to the home fans who had taken him to their hearts for two seasons. But once the match got underway, his first touch of the ball was met with boos.
Raya saved Arsenal
Sporting came extremely close to scoring in the opening minutes of the match. Ousmane Diomande's deep ball - with an outside edge - cut through Arsenal's right-wing defence, reaching Maximiliano Araújo who pulled the ball hard and shot against the crossbar after David Raya got his fingertips on the ball.
Arsenal grew into the game after a slow start. Noni Madueke hit the crossbar from a corner and Martin Ødegaard shot wide.
Martín Zubimendi placed what he thought was Arsenal's opening goal, but Gyökeres was in a clear offside position before it and the goal was ruled out.
Raya saved Arsenal again in the final stages when he headed a corner kick.
Shortly after, Havertz took Arsenal a good step closer to the semi-finals.
The return leg will be played in London on Wednesday next week. Sporting will then have to do without suspended striker Luis Suárez.
