Benfica's clash with Sporting Lisbon was eagerly anticipated but the game at Estadio da Luz never even got started after parts of the stadium roof fell off in high winds.
Insulation material began falling from the roof prior to kick-off as winds battered the Portuguese capital.
But from there, Paulo Fonseca's side were still forced to work hard for their triumph, not sealing the result until two goals in the last three minutes as first Jackson Martinez netted in the 87th minute and then substitute Ricardo Pereira added a third goal in stoppage time.
Diogo Viana pulled a goal back just after the hour mark but Colombian Felipe Pardo quickly restored Braga's two-goal lead.
Cesar Peixoto was then sent off with 21 minutes to play before Pardo grabbed his second, and Braga's fourth.
Other results on Sunday saw Oumar Diakhite's 89th-minute leveller give Olhanense a 1-1 home draw against Maritimo, while Arouca also left it late to snatch a point, with Tunisia international Lassad Nouioui scoring an injury-time equaliser in a 1-1 draw at Rio Ave.
