Bayern will face either their fellow German rivals Bayer Leverkusen or Spanish giants Atletico Madrid in the last 16.
Celtic had led 1-0 since the 63rd minute and the Scottish side had been on the verge of taking the German giants to extra time and pulling off their first ever win in Germany.
But with Harry Kane off injured and time running out, Davies stepped up as Bayern’s saviour, tapping in after Celtic keeper Kasper Schmeichel had kept out Leon Goretzka’s header.
“We had the ball on the edge of the box, so I just went into the box and didn’t think too much, just put a foot out and it went in,” said an elated Davies.
“This is football. The scoreline is what it is. The most important thing is that we advanced.”
“I’m very happy to get another goal in the Champions League” said Davies who had missed three of Bayern’s four previous games in the competition.
“It’s impressive, he worked hard with the rehab team and medical team,” said coach Vincent Kompany. “We’ve immediately seen what he offers for the team.”
Bayern went into this game 2-1 up from last week’s first leg at Celtic Park and seeking to stretch their unbeaten run to seven games in all competitions.
Bayern dominated possession in the first half but Celtic were more dangerous with at least three clear cut chances to score before the break.
Former Bayern Munich second-team player, Nicolas Kuehn, beat Manuel Neuer but Raphael Guerreiro cleared off the line.
Moments later, Alistair Johnston flashed a dangerous ball across the Bayern goal. With Neuer stranded the ball flew just beyond Daizen Maeda.
Then Maeda missed a golden opportunity to put Celtic ahead. When Dayot Upamecano was forced into a stray pass, Kuehn led the surge forward and fed Maeda, who blazed over with Kuehn and Jota in support.
Bayern dominated the ball on a freezing night but suffered with a lack of quality in attack.
Serge Gnabry was wasteful while Kane sometimes cut an isolated figure, starved of service.
‘Intensity’
