Euro 2024 winner Nico Williams grabbed a vital brace as Bilbao overturned a one-goal first-leg deficit to progress 4-3 on aggregate against the Italians.
The tie swung dramatically in the hosts’ favour in the 11th minute when veteran Roma centre-half Mats Hummels received a straight red card for a last-man tackle on Maroan Sannadi.
Bilbao cranked up the pressure and finally found the breakthrough they were so desperately craving three minutes into first-half additional time.
Inaki Williams’ cross from the left travelled all the way across the box to his brother at the back post who shot first time, his goalbound effort taking a wicked deflection off Angelino to beat Mile Svilar.
A bullet Yuri Berchiche header from a corner gave the Basques a 2-0 lead in the 68th minute at the San Mames and Nico Williams grabbed a fine second eight minutes from time.
A 93rd-minute penalty by Leandro Paredes gave the Romans hope in the final seconds, but Bilbao held firm.
It was a better evening for fellow Italian capital club Lazio, who progressed 3-2 on aggregate against Viktoria Plzen.
Pavel Sulc levelled the tie for the Czechs shortly after half-time, but Alessio Romagnoli nodded in a corner with 19 minutes remaining to tie the score at 1-1 in the Stadio Olimpico and send Lazio through.
Elsewhere in the Europa League, goals by Jean-Matteo Bahoya and Hugo Ekitike, as well as a Mario Goetze brace, handed Eintracht Frankfurt a 4-1 home win against Ajax.
The German side progressed to the next stage with a 6-2 win over both legs.
Norwegians Bodo/Glimt lost 2-1 against reigning Europa Conference League champions Olympiakos in Athens, but went through 4-2 on aggregate.
