Roma, who drew 1-1 in Portugal, started as favourites but never recovered after Felipe gave the visitors an eighth-minute lead and the Italians imploded when Daniele De Rossi and Emerson Palmieri were shown straight red cards either side of halftime.
Monaco joined Porto in advancing with a 1-0 win over Villarreal, a 90th-minute penalty by Fabinho securing a 3-1 aggregate victory.
Legia Warsaw, Celtic and Ludogorets Razgrad also qualified for the group stage, although none of them won on the night.
Poland's Legia drew 1-1 at home to Dundalk but progressed 3-1 on aggregate, Celtic squeezed past Hapoel Beer Sheva 5-4 on aggregate despite a 2-0 loss in Israel and Ludogorets held Viktoria Plzen 2-2 away to complete a 4-2 aggregate win.
(Reporting by Brian Homewood, editing by Ed Osmond)
