Braga winger Ricardo Horta capitalised on a mistake from Ryan Bennett to inflict a 1-0 defeat on Wolves in their Europa League opener on Thursday.
Wolves scored at least two goals in each of their six qualifying matches but failed to find a way through their Portuguese visitors and were dealt a sucker punch 19 minutes from time.
Horta fired home the only goal of the game at Molineux after Bennett's pass was cut out just inside the opposition half.
The Premier League side had looked the more likely side to snatch the win before Horta's strike against the run of play, but Patrick Cutrone and Leander Dendoncker squandered promising opportunities as Wolves' Group K campaign began with a defeat.
Nuno Espirito Santo's team were competing in a major European competition for the first time since 1980-81 and they edged the first half, Cutrone blazing over and dragging wide from the best of their openings.
Braga, who like Wolves have made a slow start to their domestic campaign, were denied a penalty between those missed chances when Galeno went to ground under slight contact from Conor Coady.
Dendoncker went close to finding the breakthrough six minutes into the second half with a drilled effort that was saved by goalkeeper Matheus.
But Braga took a step towards all three points after Galeno intercepted Bennett's ball down the line and advanced on the left before squaring to Horta, who took a touch and blasted past Rui Patricio.
Wolves desperately pushed for a leveller, but Matheus was equal to efforts from Willy Boly and Ruben Neves in the closing stages.