MUNICH, Germany - Bayern Munich's Alphonso Davies snatched a last-gasp equalizer against Celtic for a 1-1 draw in their playoff on Tuesday as they reached the Champions League last-16 by 3-2 on aggregate.

They will next face either fellow Bundesliga side Bayer Leverkusen or Atletico Madrid depending on Friday's draw.

Davies scored in stoppage time after former Bayern reserve player Nicolas Kuehn had given the visitors a shock lead in the 63rd minute as they tried to overturn a first-leg deficit and win a first game in Germany in 16 attempts.

Having lost the first leg 2-1 in Glasgow, Celtic came agonizingly close to forcing extra time with a bold performance that had the hosts on the backfoot for much of the game.

"If you watched the first leg, I don't think it was surprising," said Bayern midfielder Leon Goretzka. "Of course we could have made it easier for ourselves by not conceding a goal."

"We have played three games in six days now and it was all about getting results, which we did and we're happy about that," he added after Bayern earned a 0-0 draw at reigning German champions Leverkusen on Saturday.

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With the Bavarians made to sweat from the start, Celtic's Kuehn saw a shot cleared off the line by Raphael Guerreiro in the 16th minute before Daizen Maeda narrowly missed connecting with an Arne Engels cross in front of goal a little later.

Bayern had to wait until the stroke of halftime for their own opportunity, striker Harry Kane hitting the bar with a shot.

The England captain, who had little impact otherwise and was nursing a knock to the head from the Leverkusen game, was taken off at halftime.

Kuehn pounces

Bayern came close again seconds after the restart with Goretzka failing to beat goalkeeper Kasper Schmeichel in a one-on-one.

It was Celtic, however, who broke the deadlock with a deserved goal when Kuehn slotted home following two defensive errors to put Brendan Rodgers' team in the driving seat.

Bayern upped the tempo and came close with Goretzka and Leroy Sane before Schmeichel pulled off another superb save to deny Joshua Kimmich.

The Dane then did everything right to stop Goretzka's effort in front of goal in stoppage time but could do nothing when Davies bundled the ball over the line on the rebound.

The equalizer sent the Germans through to the knockout stage and left Celtic's players and coach bitterly disappointed.

"It was just such a cruel way to not even lose the game but to go out of the competition," said Rodgers. "A real heroic performance, just unfortunate at the end.

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"I think our European credibility has been restored this season, I think we built that up from last year, that's my takeaway from this season."