Despite taking the league through Bojan Miovski, the home side equalised in the final moments of the first-half before Barnabás Varga found the winning goal in the second-half.
There were two changes from the weekend’s victory over Kilmarnock as captain James Tavernier and Danilo came into the starting XI.
Rangers lined-up with Jack Butland in goal behind a defensive line of Max Aarons, James Tavernier, Nasser Djiga, Emmanuel Fernandez and Jayden Meghoma.
Connor Barron and Nico Raskin were in midfield, while Danilo joined Bojan Miovski and Djeidi Gasssama in attack.
The Hungarian side have had a good start to European competition this season, unbeaten in the opening five fixtures in the league phase.
It was a fairly even opening quarter of an hour in this match, with Bamidele Yusuf going just wide with an early effort for Ferencváros.
However, with 27 minutes played, it was Rangers who had the breakthrough in Budapest. It was another good move from the Light Blues as Gassama played the ball out to Max Aarons on the right. He delivered a dangerous ball into the box, with Danilo’s initial effort blocked, Bojan Miovski produced an acrobatic finish to send the ball into the back of the net.
Initially disallowed for offside, a VAR check overturned the decision as Miovski ran off to celebrate his third goal in two games.
With 20 seconds remaining of first-half injury time, the home side had their equaliser. Ibrahim Cissé picked the ball up in the box and cut it back to Bence Ötvös who was in space just inside the area and he finished a low right-footed shot beyond Butland to draw the game level at the break.
Into the second-half, Barnabás Varga raced towards goal early in the half as he broke up the pitch with pace, but Nasser Djiga recovered well to get a good challenge in and deny the hosts’ top goalscorer this season a sight of target.
Danny Röhlturned to his bench for the first time in this match, with 58 minutes played. It was a big moment for Dujon Sterling as he returned to the pitch for the first time since April after a lengthy rehab for an achilles injury, while Mikey Moore came on to replace Djeidi Gassama.
Rangers were forced into another change shortly after as Bojan Miovski appeared to come off with an issue and was replaced by Youssef Chermiti. Findlay Curtis was also introduced for Danilo.
The home side took the lead for the first time this evening with just under 20 minutes remaining in this match. Callum O’Dowda delivered a ball deep into the box from the left-hand side and Barnabás Varga broke free from Emmanuel Fernandez to finish at the back post.
Rangers were denied an equaliser with 87 minutes played as the ball broke for Findlay Curtis and he released a powerful strike at goal but Gróf was down to his left to pull off a good save.
RANGERS: Butland, Tavernier (Aasgaard, 75), Djiga, Fernandez, Meghoma, Aarons (Sterling, 58), Raskin, Barron, Danilo (Curtis, 66), Gassama (Moore, 58), Miovski (Chermiti, 66).
Subs: Kelly, Stewart, Adamson, Cameron.
Ferencváros: Gróf, Yusuf (Joseph, 74), Varga (Pešić, 89), Szalai, Ötvös (Zachariassen, 74), Makreckis, Cissé, Raemaekers, Kanichowsky (Romão, 82), O’Dowda (Cadu, 82), Tóth.
Subs: Radnóti,Levi, Gruber, Gólik, Lakatos, Madarász, , Nagy