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Liverpool did enough to build themselves a solid lead for Tuesday's return game in Spain where they will be confident of finishing off the job.
There were a few nerves at the end but Liverpool set up a Champions League semi-final with Villarreal after Roberto Firmino scored twice in a 3-3 second-leg draw with Benfica on Wednesday to ensure a 6-4 aggregate win.
Six-time European champions Bayern, who had won 12 of their previous 13 home games in the competition, levelled the tie when Robert Lewandowski drilled the ball in off the post after 52 minutes with his 13th Champions League goal of the season.
Villarreal took the game to Bayern and should probably have won by a larger margin given their clear opportunities.
Having fallen before the quarterfinals against Olympique Lyonnais and Porto in the previous two seasons, in-form Juventus, who had lost just once in their last 21 matches in all competitions, were firm favourites to progress.
On the night he set the new record for the most appearances in the competition, the 36-year-old delivered the killer blow to save his manager Ole Gunnar Solskjaer from another disappointing result.
Villarreal goalkeeper Geronimo Rulli kept his composure to score in a nerve-shredding, seemingly never-ending shootout then denied David de Gea as his side won their first major trophy by beating Manchester United 11-10 on penalties.
Spanish media reported on Friday that police are investigating possible match-fixing in a 2-2 draw between the two clubs in La Liga last year.
Villarreal defender Pau Torres scored an own goal right at the end of the first half to heap more pain on Unai Emery's side.
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