Backed up by a vociferous home crowd, Athletic pressed forward early as they looked to overturn the deficit handed to them in the closing stages of the first leg.
A positive opening 10 minutes may not have produced much in the way of chances, but Roma were forced into a costly early error as experienced centre-back Mats Hummels was sent off.
After a stray square pass was intercepted by Maroan Sannadi, Hummels attempted to atone with a desperate sliding challenge on the last line, which ultimately missed its mark, resulting in his early expulsion from the contest.
Ernesto Valverde’s men looked to capitalise, but Sannadi was wasteful with a close-range chip before the dangerous Nico Williams cut in from the left and rifled against the post.
While they struggled for possession and posed no real threat, the Giallorossi coped well with their numerical disadvantage, so boss Claudio Ranieri would have been frustrated that they were undone with the final action of the first half.
Brothers Inaki and Nico Williams swapped wings in the closing stages before half-time and the move paid dividends, with Inaki’s cross from the left headed on by Sannadi into the path of Nico to turn home, albeit with a hefty deflection off Angelino.
Roma regained their composure over the break and continued to frustrate the hosts, who found clear-cut chances hard to come by following the restart.
A scare came their way when Eldor Shomurodov - hero of the first leg - came off the bench and immediately raced clear of the Roma defence only to be denied at the near post by Mile Svilar.
Normal service resumed thereafter, with Alex Berenguer forcing Svilar into an impressive save down to his left before Athletic finally edged ahead on aggregate.
The visitors were undone by a set-piece, as Berenguer’s corner was brilliantly headed into the far corner by Yuri Berchiche, whose arched effort left Svilar with no chance of making a save.
The onus to attack was now on a Roma side who had managed just three shots in the opening 75 minutes of action, but they were ultimately unable to produce enough quality in the final third.
The contest was put beyond Ranieri’s men when Nico Williams added a third, as he jinked inside Gianluca Mancini and dinked over Svilar to secure his side’s place in the last eight with a fifth successive UEL home win.
Roma bow out despite a 93rd-minute consolation penalty from Leandro Paredes, with their winless return from their last 11 UEL away games on foreign soil proving costly, leaving the Giallorossi with just Serie A to focus on.
Flashscore Man of the Match: Nico Williams (Athletic Club)