Captain Lionel Messi was the obvious absentee following his dismissal on Sunday, as Antoine Griezmann led the line with Ilaix Moriba given his first start of the season and Neto in goal.
Barca nearly had an early set-back as the host threatened from a corner-kick, but Javier Ontiveros Robles was unable to steer a flick-on from Pol Moreno past Neto.
A pin-point save from Leo Ramirez kept Barca at bay on 33 minutes when he parried a powerful volley from Francisco Trincao from good work near the area by Miralem Pjanic.
Barcelona were given a more clearer chance to go ahead five minutes later as a high foot in the area from Albert Estelles on Ronald Araujo resulted in a penalty, which Pjanic missed.
Ronald Koeman went for a substitution following the second half resumption, with Riqui Puig withdrawn for Ousmane Dembele.
Two big chances for Cornella towards the closing minutes had Cornella missing a golden chance through a rasping strike from Eloy Gila before going on to shave the post from a loose pass.
Barca won their second penalty of the match 12 minutes to the end following a foul by Moreno on Clement Lenglet, however Dembele stepped up and missed.
A late chance fell to Pjanic following a swerving attempt towards the top-corner, but Ramon sprung alive to tip for a corner, as the match headed to extra-time to determine a winner.
Dembele atoned for the penalty miss two minutes inside extra-time after Roman directed his powerful strike from a pass by Pedri in off the underside of the crossbar.
Cornella finished with ten players in the final minute of the match when Estelles received a second yellow card following a lunge on Araujo.
The Catalans made sure of progression to the last 16 when Braithwaite latched onto a square ball from Pedri to tuck home.