Wolves were left stunned by Braga's second-half revival as both sides sealed progress to the last 32 of the Europa League following a 3-3 draw.
After storming back from a goal down to lead 3-1 at the interval, Wolves somehow let maximum points and top spot in Group K slip from their grasp in a thriller in the rain in Portugal.
The visitors, unchanged from the 2-1 Premier League win over Bournemouth, fell behind after six minutes when Andre Horta's deflected effort found the back of the net in sodden conditions.
But Raul Jimenez – involved in all three of his side's goals – swiftly levelled matters with his 15th of the season before a quick-fire double from Matt Doherty and Adama Traore put Nuno Espirito Santo's men in the ascendancy.
That was far from the end of the story, though, as Paulinho cut the gap and Fransergio grabbed a late equaliser to keep Braga top. Third-placed Slovan Bratislava's 2-1 defeat at Besiktas spelled the end of road for the Slovakians, with their Turkish opponents already out of the running.
Braga won the reverse fixture with Wolves at Molineux courtesy of Ricardo Horta's goal and it was his brother who put them ahead on Thursday, Andre Horta's low strike taking a telling touch off Ruben Neves to send the ball beyond Rui Patricio.
Wolves, sitting fifth in the English top flight, were quick to respond and Jimenez headed home after Jonny's looping cross had left Eduardo flapping at thin air.
Nuno's side came close to forging ahead midway through the first half, but Traore's teasing ball across the six-yard box was just beyond the reach of Diogo Jota.
Undeterred, Wolves continued to push forward and got their reward with two goals in 81 seconds – Doherty leaping to nod in Jimenez's lofted delivery before Traore coolly slotted in the third.
A smart stop from Eduardo spared Braga further punishment as he parried away Jota's header five minutes into the second half.
The hosts lost a tearful Wallace to injury just before the hour mark but were soon celebrating halving the deficit through Paulinho's close-range finish, after excellent work from Wenderson Galeno.
Despite Wolves still appearing to carry the greater threat, they were rocked by Fransergio's 79th-minute header from Nuno Sequeira's assist as the spoils were shared in an unlikely classic.