The Bundesliga champions were expected to make light work of the struggling Red Devils in the first leg, but could only muster a 1-1 draw and saw two key midfielders pick up bans
The clubs have enjoyed contrasting fortunes domestically this season, with Bayern having already retained their Bundesliga title while English champions United languish seventh in the Premier League table.
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Bayern are without several central options through injury and suspension and were beaten for the first time in 18 months on Saturday, while United are the best away side in the English top flight and thrashed Newcastle at the weekend.
Bayern's 1-0 setback at Augsburg ended their record 53-match unbeaten run in the Bundesliga. Guardiola shrugged off the defeat, but described the second leg with United as a "life or death match".
By contrast, United were dominant in a 4-0 win at St James' Park on Saturday, though Juan Mata, who scored twice, is ineligible in Europe.
Striker Robin van Persie misses out again with a knee injury and Wayne Rooney is doubtful with a bruised toe, though Patrice Evra is back from a ban and should be fit despite going off against the Magpies.
Bastian Schweinsteiger scored Bayern's goal in the first leg but misses out here after picking up a late red card at Old Trafford. Die Roten are also without Javi Martinez through suspension, while Thiago Alcantara is sidelined with a knee problem and Xherdan Shaqiri (thigh) will also miss out.
But despite the weekend's results and Bayern's injuries, Guardiola's side should be regarded as heavy favourites to progress.
United have endured a tricky first campaign under Moyes, who replaced the legendary Sir Alex Ferguson last July, with the club now mathematically certain to relinquish their Premier League title as they sit 17 points adrift of leaders Liverpool with five games to play.
They also look likely to miss out on qualification for the Champions League for the first time since 1995-96, as they are seven points behind fourth-placed Arsenal.
Moyes has been under severe pressure in recent weeks, especially following humbling defeats at Olympiakos and at home to Liverpool and Manchester City. Some supporters even organised and paid for an aeroplane to fly over Old Trafford urging the club's board to sack the Scot.
And Bayern, despite their loss at the weekend, have continued to flourish under Pep Guardiola's guidance, with the Bavarians wrapping up the German title with seven matches to spare, while they remain on course to retain both their Champions League and DFB-Pokal crowns.
Schweinsteiger's away goal also puts Bayern in the driving seat to reach the semi-finals, with United needing to win or record a high-scoring draw of 2-2 or higher on the night.
However, United left-back Evra believes his side can emulate Chelsea's 2011-12 season, when the London club finished sixth in the Premier League but won the Champions League.
"It was funny because the season reminded me of the Chelsea season when they won the Champions League when they were not playing well in the league," Evra told reporters.
"I am not saying we are going to do the same but sometimes you have to be positive, so why not?
"Of course it is unusual for us to say we can save our season in one game. Now we must make sure the fans will be proud for the second leg against Bayern."