Hansi Flick's side booked their place in the last four of this season's competition by beating Barcelona 8-2 in a thrilling encounter in Lisbon on Friday night.
Bayern found themselves 4-1 up with only 31 minutes on the clock at Estadio da Luz, as a Thomas Muller brace and goals from Ivan Perisic and Serge Gnabry left Barca, who scored an early equaliser via David Alaba's unfortunate own goal, on the brink of elimination.
A superb Luis Suarez effort ten minutes into the second half gave the Blaugrana hope, which was cruelly dashed moments later when Kimmich tapped in from close range following a scintillating Davies run down the left-wing.
The Canadian full-back skipped past Arturo Vidal before easily beating Nelson Semedo with a combination of pace and guile, and laid the ball on a platter for his colleague to restore Bayern's three-goal advantage.
A Robert Lewandowski header and a late double from Barca loanee Philippe Coutinho against his parent club rounded off the scoring, as the German champions set up a last-four showdown against either Manchester City or Lyon.
When asked to discuss Davies' contribution to Bayern's fifth goal, Kimmich told reporters post-match: "Unbelievable. I was almost ashamed of how happy I was after the goal because it was 99 per cent, of course, his goal.
"In the end, I just had to push it in. World-class."
Flick added on the 19-year-old defender's remarkable surge into the box: "Simply beautiful. He has the quality. If he does it more often, it would be all the more beautiful."
Bayern have now won 19 games on the bounce in all competitions, and are on course to emulate Jupp Heynckes' 2012-13 treble-winning squad by securing the club's sixth European Cup later this month.
The showpiece event could yet be an all-German affair on August 23, with RB Leipzig and Paris Saint-Germain set to meet in the first semi-final tie next Tuesday, before Flick's men take centre-stage a day later.