
Florian Grillitsch gave the hosts an early lead with a deft near-post backheel before Cucho Hernandez levelled from the spot for Betis in the second half to leave the tie delicately poised ahead of next Thursday’s return leg in Seville.
In the round of 16, both sides produced four-goal performances in the second legs of their respective ties to come from behind and qualify.
Braga seized the advantage at their picturesque Estadio Municipal home in the fifth minute as Austrian Grillitsch darted to the front post from a low corner and turned a slick backheel past Pau Lopez in the Betis net.
At the other end, Braga goalkeeper Lukas Hornicek was in excellent form as he produced fine saves to deny Marc Bartra, Abde Ezzalzouli and Hernandez in the first period.
The Czech’s resistance was broken on 61 minutes, however, as Colombian Hernandez sent him the wrong way from the spot after Jean-Baptiste Gorby had scythed down Ezzalzouli in the box.
The other quarter-final first legs take place on Thursday with Premier League strugglers Nottingham Forest making the trip to Portugal to take on Porto.
Aston Villa visit Coppa Italia winners Bologna and Freiburg welcome Celta Vigo.