Nuno Espirito Santo’s side arrived at the Estadio Municipal de Braga a point behind the hosts and Group K leaders, needing a point to progress with a game to spare.
And they claimed the point they needed from an exciting encounter that saw them fall behind early after Andre Horta’s opener.
Goals from Raul Jimenez, Matt Doherty and Adama Traore then saw the visitors race into a 3-1 lead.
But second-half goals from Paulinho and captain Fransergio rescued Braga to also send them into the last 32.
Meanwhile, Rangers climbed to the top of Europa League Group G in another exciting clash as Alfredo Morelos’ record-breaking double secured a 2-2 draw with Feyenoord.
The Colombian became the first Rangers player to score in four consecutive European clashes when he cancelled out Jans Toornstra’s opener in Rotterdam.
Morelos then left De Kuip stunned as he struck his 13th European goal of the campaign shortly afterwards to smash Henrik Larsson’s 16-year-old record for the most goals netted in a single season for a Scottish club.
Steven Gerrard’s men were on the brink of securing a place in the knock-out rounds but Morelos’ international colleague Luis Sinisterra grabbed an equaliser for Dick Advocaat’s team.
The Gers will reach the knockout stages if they draw with Young Boys at Ibrox.
Meanwhile, Celtic ensured they will top Group E with a game to spare after a 3-1 victory over Rennes at Parkhead.
The victory, coupled with Lazio’s 1-0 victory over CFR Cluj, means Neil Lennon’s side will avoid Champions League dropouts in February’s last 32.
Lewis Morgan and Ryan Christie put the hosts in complete control, before Mikey Johnston added to their tally with a superb one-two finish.
Adrien Hunou’s glancing header provided a late consolation for the French side.
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