Arsenal's Champions League hopes were snuffed out as Joshua Kimmich's bullet header was enough to take Bayern Munich into the semi-finals.
After an enthralling 2-2 draw at the Emirates Stadium last week, this tie was finely poised but it was the hosts who progressed as Kimmich headed home in the second half to seal a 1-0 win for Bayern.
Thomas Tuchel became just the second man to lead three different clubs into the last four of the Champions League and his side are now closing in on a Wembley final on 1 June.
Bayern showed the sort of pedigree in the competition that comes from years of being involved in the business end of the tournament - they have now qualified for 13 semi-finals and have reached the stage nine times since Arsenal's last semi-final appearance in 2009.
Arsenal, in fact, have never won an away Champions League game from the quarter-final stages onwards and they failed to turn in the sort of performance here that would change that.
Having lost 2-0 at home to Aston Villa on Sunday to dent their Premier League title hopes, their European exploits came to a shuddering halt as Bayern's nous eventually saw them advance.
The win also maintained England captain Harry Kane's chances of winning silverware in his debut season in Germany, the former Tottenham striker missing out on a Bundesliga title following Bayer Leverkusen's remarkable campaign.
Kane had a quiet evening after half a chance in the opening exchanges and it was Arsenal who enjoyed a good spell as they looked to take the lead in the tie.
Gabriel Martinelli flashed a shot wide before wiggling through a couple of challenges only to come up against the imposing presence of Bayern skipper Manuel Neuer in the hosts' goal.
At the other end, David Raya was called into action for the first time as he saved from Jamal Musiala following a speedy Bayern break.
Neuer's first meaningful action of the night saw him paw a deflected Martin Odegaard shot off target as he sprang up to prevent the ball running behind for a corner.
Martinelli then missed a great chance to open the scoring just after the half-hour, shooting straight at Neuer when picked out free in the Bayern box.
Bayern were fuming as they looked to catch Arsenal out after Bukayo Saka was down needing treatment and Mikel Arteta gathered his players on the touchline only for the winger to clamber to his feet.
A quick throw-in with all of the Arsenal side distracted was instead pulled back by referee Danny Makkelie, much to the chagrin of the home fans.
Bayern were second best for the majority of a largely passive first 45 minutes for the hosts, but straight after the restart they were on it, hitting the crossbar through a Leon Goretzka header before Raphael Guerreiro's follow-up deflected against the post.
Arsenal were slightly rattled and Gabriel Magalhaes passed the ball out of play for a corner following a breakdown in communication with Raya.
Arsenal survived the resulting set-piece but fell behind soon after, Kimmich flying past a slow-moving Martinelli to power Guerreiro's cross into the back of the net.
Arteta reacted almost immediately by turning to his bench, bringing on Gabriel Jesus and Leandro Trossard but Arsenal's race appeared to be run.
They struggled to create any chance of note in chasing the game, taking more and more risks at the back in doing so.
This may not have been a repeat of Arsenal's two previous visits to the Allianz Arena, both 5-1 defeats, but it showed Arsenal are still a step below Europe's elite.
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