Brazilian substitute Maicosuel tried to emulate Andrea Pirlo's effort for Italy against England at Euro 2012 by nonchalantly chipping the ball into the middle of the goal but mis-hit his shot and allowed Braga's goalkeeper Beto to save.
Spain's Malaga, facing uncertainty behind the scenes amid speculation that their Qatari owner is looking to sell up, overcame their internal worries to reach the group stage for the first time after drawing 0-0 at Panathinaikos.
Anderlecht qualified for the first time since 2006/07 with a 2-0 win over AEL Limassol, denying the Cypriot champions a chance to emulate APOEL Nicosia who reached the quarter-finals last time.
The Belgians were joined in the group stage and Thursday's draw in Monaco by BATE Borisov of Belarus and Croatia's Dinamo Zagreb, who both qualified for the second year running.
Portuguese side Braga's collection of Brazilian journeymen won 5-4 on penalties against shattered Udinese after the two sides drew 1-1 for a 2-2 aggregate draw.
Udinese also paid the price for selling three of their top players from the previous season, goalkeeper Samir Handanovic going to Inter Milan while Mauricio Isla and Kwadwo Asamoah joined Juventus.
Beaten by Arsenal at the same stage last season, Udinese made a jittery start against opponents wearing the same colour strip as the English side but went ahead after 25 minutes.
Dusan Basta hooked a cross into the area and Pablo Armero dived in to head the ball beyond goalkeeper Beto.
The Colombian also had a golden chance to add a second early in the second half when he had a free shot on goal but, in a moment of pure slapstick, slipped over as he took aim.
Braga, whose side includes seven Brazilians who are mostly well-travelled and have plied their trade at unglamorous clubs, were in control by then and levelled when substitute Ruben Micael headed in Mossoro's cross in the 72nd minute.
Udinese's defeat means Italy will have only Serie A champions Juventus and seven-times European Cup winners AC Milan in the group stage.
Malaga have seen Spain midfielder Santi Cazorla and Venezuela striker Salomon Rondon depart for Arsenal and Rubin Kazan respectively in what the Andalusian club has described as a process of "internal restructuring".
However, they held on comfortably in Athens in a game of few scoring chances against opponents who have taken part in the group stage nine times.
Democratic Republic of Congo forward Dieudonne Mbokani and Ukraine forward Oleksandr Yakovenko scored in the last 10 minutes for Anderlecht.
Mbokani drove in Massimo Bruno's cross in the 81st minute to end some tenacious resistance by AEL's cosmopolitan side and Yakovenko scored inside the far post as he finally netted after being repeatedly denied earlier in the game.
Anderlecht's 3-2 aggregate win allowed them to take what many felt to be their rightful place in the group stage for which they had originally qualified.
The Belgians were demoted to the third qualifying round after Chelsea's Champions League title last season following a sixth-place Premier League finish forced UEFA to reshuffle the places.
The changes also led to Tottenham Hotspur losing their berth and being moved into the Europa League.
BATE Borisov, full name Borisov Works of Automobile and Tractor Electric Equipment, ploughed into the group stage with a 1-1 draw at Israeli champions Hapoel Kiryat Shmona, which gave them a 3-1 aggregate win.
Laszlo Lencse curled in a free kick for the Israel side in the 67th minute and BATE survived some anxious moments before Aleksandr Pavlov snatched a stoppage time equaliser on the break.
An early goal by Portuguese midfielder Tonel gave Dinamo Zagreb, Croatian champions for the last six seasons, a 1-0 win at Maribor in neighbouring Slovenia and sent them through 3-1 on aggregate.
The remaining Champions League play-offs take place on Wednesday.
- Dinamo Zagreb