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Favourites Barca lost 2-1 in Scotland after Victor Wanyama netted with a first-half header and Tony Watt stroked home on 83 minutes in a famous win for the modest Scottish champions who almost shocked the Catalans last time out.
Lionel Messi pulled one back late on but the point that would have put the Group G leaders through was not forthcoming even if they still lead Celtic by two points and Benfica, 2-0 winners over Spartak Moscow, by five with two to play.
United came from behind to win 3-1 at Portugal's Braga after a Robin van Persie strike, Wayne Rooney's penalty and Javier Hernandez's goal in the final 10 minutes secured a berth in the first knockout stage as group winners after a painful early exit last term.
A powercut after Alan's opening penalty for the hosts had held up the game for around 10 minutes in the second half but United roared back.
Galatasaray's 3-1 win in Cluj left the second spot wide open in Group H.
Shakhtar Donetsk could have gone through with a win in Group E but lost 3-2 at holders Chelsea, who netted late through Victor Moses following Willian's excellent double for the visitors.
Juventus won 4-0 at home to Nordsjaelland but stay third on six points with the Ukraine and English sides both on seven.
Peruvian striker Claudio Pizarro shone even more than Brazilian Willian by scoring a 15-minute first-half hat-trick to help hosts Bayern batter Lille 6-1 and top Group F with nine points alongside Valencia, 4-2 victors at home to BATE Borisov.