Bayern's quarter-final first leg success came in the middle of what coach Louis van Gaal has labelled the "weeks of truth" with their German championship chances essentially being decided in the next two games.
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The Bavarians, who are also in the German Cup final, face Bundesliga leaders Schalke 04 on Saturday and then fellow title contenders Bayer Leverkusen with the United return leg squeezed in between.
"This win was hugely important for our confidence," said Bayern chairman Karl-Heinz Rummenigge.
"Now we should not think of the return leg next Wednesday but our minds should be just on Saturday."
Bayern have suffered two consecutive league defeats and are two points behind Schalke and three ahead of Leverkusen.
The battling win against United, with Bayern coming back from a goal down to score twice in the second half, including Ivica Olic's last-gasp winner, sent a warning to their domestic rivals.
"We are still competing for three titles and I want to win all of them," Van Gaal said before the United match.
They must now show the fighting spirit exhibited on Tuesday but lacking in their league defeats to Eintracht Frankfurt and VfB Stuttgart to remain in contention for a treble of titles.
The confident talk is in stark contrast to 12 months ago when Bayern were out of the running for the league title and suffered a humiliating 5-1 aggregate defeat to Barcelona at the same stage of the Champions League.
"We now have a chance to go past United," Van Gaal told reporters, quick to point out that Bayern are going into the Schalke match with no injury concerns.
Despite Bayern eyeing a last four place in the Champions League for the first time since they won the competition in 2001, the domestic title has been more on the coach and board's mind as van Gaal consistently played down his team's chances against United.
For this reason, Dutch winger Arjen Robben did not play on Tuesday, with van Gaal fearful a minor muscle injury could worsen and his best player this season could end up missing the key Bundesliga matches.
