Roma had a goal disallowed for offside, while Ajax dominated possession without really threatening, as the 2-1 first leg result still holds in the Europa League quarter-final.
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The winners will go on to face Manchester United or Granada in the semi-finals.
The Giallorossi won the first leg 2-1 in Amsterdam, with Pau Lopez saving a Dusan Tadic penalty. Leonardo Spinazzola joined Chris Smalling, Marash Kumbulla, Stephan El Shaarawy and Nicolò Zaniolo on the injury list, with Bruno Peres suspended, but Henrikh Mkhitaryan and Rick Karsdorp returned from the start. Ajax had Devyne Rensch and Andre Onana banned, with Daley Blind and Nousasair Mazraoui injured, while Sebastien Haller was accidently left off the UEFA list. Perr Schuurs was only fit for the bench, but Maarten Stekeleburg was back in goal against his old club.
Lorenzo Pellegrini’s finish on the counter-attack was too weak to cause problems, and Jordan Veretout was offside when putting the ball in the net after eight minutes.
Pau Lopez almost gifted Ajax a goal with his terrible pass out from the back, but Amadou Diawara flung himself in the way to block the Tadic strike.
Tadic also tested Pau Lopez from eight yards on a Sean Klaiber pull-back, but it was during that move that the full-back sustained a muscular injury and had to come off.
While it was open for the first 25 minutes, Roma increasingly sat deep and stopped managing to get away on the counter, allowing Ajax over 70 per cent possession in the first half.
Roma 0-0 Ajax (Half-Time, 2-1 agg)
Roma: Pau Lopez; Mancini, Cristante, Ibanez; Karsdorp, Veretout, Diawara, Calafiori; Pellegrini, Mkhitaryan; Dzeko
Ajax: Stekelenburg; Klaiber (Schuurs 22), J Timber, Martinez, Tagliafico; Alvarez, Klaassen, Gravenberch; Antony, Tadic, Neres
Ref: Taylor (ENG)