Late goals from Robin van Persie, Wayne Rooney and Javier Hernandez saw Manchester United come from behind to secure victory in Braga and with it their place in the last 16 of the Champions League.
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A United side showing six changes from Saturday's Barclays Premier League win over Arsenal struggled to get going in the first half and the hosts went in front shortly after the interval through a penalty from Alan.
However, as they have done so often this term after conceding the first goal, the Red Devils fought back to win thanks to substitute Van Persie's 80th-minute effort from outside the box, a Rooney spot-kick five minutes later and Hernandez's stoppage-time strike.
It leaves Group H leaders United on 12 points and guaranteed to go through as group winners, with Galatasaray and Cluj on four points each and Braga on three after four rounds of matches.
Braga had caused United plenty of problems early on at Old Trafford last month, racing into a 2-0 lead inside the opening 20 minutes before eventually going down 3-2, and in the spectacular surroundings of the Estadio AXA the Portuguese side once again made the better start.
Eder nipped ahead of Jonny Evans in the sixth minute and flashed the ball across the face of goal, with no-one around to meet it.
Leandro Salino and Ruben Micael then unleashed shots that went off target before the latter caught a lofted pass with a volley that went over.
Braga went the closest yet to making a breakthrough in the 22nd minute when Eder sent a header crashing against the post, and former Newcastle man Hugo Viana struck wide soon after.
United were unable to fashion much from the possession they were having, but did register an effort on goal on the half-hour mark when Evans' tame header from Antonio Valencia's cross was easily caught by home goalkeeper Beto.
Braga were soon back on the attack, with Alan drilling low into David de Gea's arms, and the Spaniard then gathered a free-kick from Viana on his line after the fit-again Chris Smalling - making his first appearance of the season - had been booked for fouling Eder.
Nani nodded goalwards from another Valencia cross just before the interval, but again it did little to trouble Beto.
Four minutes into the second half, United were behind after Custodio collided with Evans in the box.
The referee pointed to the spot and Alan - who had scored Braga's two goals in the reverse fixture last month - made no mistake, smashing the penalty into the roof of the net.
As United looked for a response, a power cut at the stadium saw some of the floodlights go out and play was suspended for around 15 minutes.
United boss Sir Alex Ferguson used the unscheduled break to substitute Evans for Rio Ferdinand and after play resumed, De Gea got down to push away a free-kick by Nuno Coelho.
Ferguson swiftly made further adjustments, introducing Van Persie for Danny Welbeck and Rafael for Nani.
The reshuffle certainly had the desired effect, with Van Persie notching his 11th goal of the season with 10 minutes of normal time remaining, the Dutchman expertly guiding the ball over Beto, who had rushed out too soon and was attempting to get back to his line.
Rooney was then brought down in the box by Nuno Coelho and, having taken his time to decide, the referee again awarded a penalty.
Unlike against Arsenal, the England forward converted his spot-kick to hand United the advantage, and Hernandez completed the turnaround at the death, prodding the ball in at the second attempt after his initial shot had been blocked on the line.