The Spaniards reached the knockout phase when Lille's 2-0 win at BATE Borisov in the early kick-off ended the Belarussian champions' hopes and Bayern progressed despite failing to make their numerical advantage count at a raucous Mestalla.
The hosts had right-back Antonio Barragan sent off for a wild tackle on David Alaba in the 33rd minute but produced a battling performance to thwart the side that beat them on penalties in the final in Milan 11 years ago.
A deflected shot by Algeria midfielder Sofiane Feghouli fired Valencia ahead against the run of play in the 77th before Bayern's Thomas Muller levelled five minutes later.
"We definitely deserve to go through," Feghouli said in an interview with Spanish broadcaster TVE.
"We gave it our all against a great team and we are very, very pleased," added the 22-year-old, who had to revert to right-back after Barragan's dismissal.
"For my club and my team I am ready to play in whatever position the coach wants and give my all and I am very satisfied with the job I did today," he said.
"It's a good result against them but we wanted to win for our fans. Now we have to beat Lille and see if we can finish top of the group."
"We can be happy with the result but not with our performance," Bayern CEO Karl-Heinz Rummenigge said on the club's website.
"If you play with an extra man for an hour and have to be content with a 1-1 draw it's not satisfactory," added the former Germany forward. "We have to turn the corner now and put our foot on the gas again."
The Spain striker, who has four goals in the competition this season, struck a fierce shot towards Neuer's goal but it flew narrowly over the bar.
Feghouli capped a fine performance when he evaded several tackles and fired off a shot that was deflected into the net off Dante's arm before Germany midfielder Muller's scuffed effort for Bayern secured the late equaliser.
Valencia's morale-boosting performance while a
