Patrick Cutrone blew two good chances as Wolves' winning streak in Europe came to an abrupt end and their troubles grow.
Nuno Espirito Santo's men qualified in style for Group K with six wins on the spin.
But Wolves , who are yet to win in the Premier League this term, were beaten again at home after being thumped by Chelsea at the weekend.
It was the club's first appearance in a major European competition since the 1980-81 UEFA Cup.
But Braga, 16th in the Portuguese top tier just one place above the drop zone, spoiled the night.
Wolves were left to rue Italian summer signing Cutrone missing the target with two first half efforts.
Ricardo Horta, who is pals with Wolves' Portuguese compatriot Ruben Neves, later punished the hosts 19 minutes from time with a clinical finish on the break.
Defeat condemned Nuno's men to a worrying third straight defeat in all competitions as their woes continue to grow with the club languishing 19th in the Premier League.
And though the club and their stars repeatedly deny it, playing in Europe appears to be overloading the side who shone last term and came seventh.
Wolves (3-5-2): Patricio 6; Bennett 6, Coady 6, Boly 6; Doherty 6 (Traore 80, 6), Dendoncker 6 (Jota 76, 6), Neves 6, Gibbs-White 6 (Moutinho 67, 6), Jonny 6; Jimenez 6, Cutrone 5.
Braga (4-1-4-1): Matheus 7 Booked; Esgaio 7, B Viana 7, Santos 7, Sequeira Booked 7; Palhinha 6; Galeno 7 (Trincao 84,6), A Horta 6 (Novais 86,6), Fransergio 6, R Horta 8 (Costa 88 Booked, 6); Paulinho 6.
Man of the match: Ricardo Horta. Took his goal clinically
Referee: Jakob Kehlet (Denmark) 7 Attendance: 28,314
