Lyon's goalkeeper pulled off a string of spectacular saves throughout a tremendous contest at Stadio Olimpico as the Ligue 1 team progressed despite losing 2-1 on the night.
In a game which matched the first leg of this classic European tie for its remarkable intensity, Roma hit the woodwork through Antonio Rudiger in an action-packed opening before Mouctar Diakhaby put Bruno Genesio's men ahead.
Roma immediately pulled level through Kevin Strootman's fortunate finish, but Lopes was on hand to twice deny the midfielder a second as the half wore on.
Lucas Tousart's own-goal on the hour-mark set-up an enthralling finish as Roma laid siege to Lyon's goal - Stephan El Shaarawy going closest to what would have been a decisive strike, while Edin Dzeko had a goal ruled out for a marginal offside call.
Maxwel Cornet squandered two gilt-edged opportunities at the other end, but those misses mattered little in the end as, in spite of a late Roma onslaught, Lyon's defence held firm to secure a famous win.
Roma were on top in a blistering opening to the second leg - Rudiger rattling the crossbar from close range before Lopes twice denied Mohamed Salah.
For all their dominance though, Roma found themselves behind after 16 minutes.
In a near carbon-copy of his goal from the first leg, Lyon youngster Diakhaby capitalised on poor Roma marking to head home powerfully from Mathieu Valbuena's free-kick.
Lyon's lead was cancelled out within a minute, however, as Strootman managed to bundle the ball over the line after connecting with a fantastic Daniele De Rossi delivery.
Lopes came to Lyon's rescue again as the interval approached, pulling off a stunning double save to prevent Strootman doubling his and Roma's tally before reacting instinctively to keep out Dzeko's strike.
Lyon's shot stopper continued in the same vein after the restart, making another superb series of saves - from Nainggolan and Dzeko respectively - to keep the score level.
Valbuena should have put the result beyond all doubt a few moments later, but the former Marseille playmaker somehow skewed his effort over from point-blank range.
Genesio's side were then made to pay for that miss, substitute El Shaarawy making an immediate impact as his low cross deflected in off the unfortunate Tousart.
El Shaarawy could have completed a quick-fire turn-around, but the winger failed to find the bottom corner after engineering space for himself in the area, before Cornet blazed over at the other end.
Cornet had the opportunity to atone for his miss late on when, after Dzeko had seen a goal disallowed for a close offside call against El Shaarawy, he raced through unchallenged, only to allow Alisson to dive in and smother the chance.
Despite Cornet's wastefulness, though, Lyon rallied to survive a late glut of Roma pressure - led by veteran Francesco Totti - and seal a place in the last eight.