The Spanish giant was held to a 0-0 draw at home by the Turkish club in the first leg last week.
Pierre-Emerick Aubameyang scored the winning goal for Barcelona to secure a 2-1 victory over Galatasaray and send the struggling European powerhouse into the quarterfinals of the Europa League.
Aubameyang netted from close range four minutes into the second half on Thursday as Barcelona came from a goal down to maintain its chances of ending the season with a trophy.
The Spanish giant, which is playing Europe’s second-tier competition after failing to advance to the Champions League knockout stages for the first time since 2004, was held to a 0-0 draw at home by the Turkish club in the first leg last week.
Rangers reached the quarterfinals on a 4-2 aggregate score despite losing 2-1 to Red Star at Belgrade. Atalanta also advanced 4-2 on aggregate after winning 1-0 at Bayer Leverkusen while Portuguese club Braga progressed after holding Monaco 1-1.
Another Spanish team, Sevilla, takes a 1-0 lead into its second leg against West Ham later Thursday.
In the inaugural Europa Conference League, Leicester advanced 3-2 on aggregate despite a 2-1 away loss to Rennes.
Marseille, PSV and Bodø/Glimt also made the quarterfinals.
Jose Mourinho’s Roma was playing Dutch side Vitesse later.
EUROPA LEAGUE
Barcelona, which also needed an away win at Napoli just to reach the round of 16, looked to be in trouble when Marcão headed in the opener for Galatasaray off Alexandru Cicâldau’s corner in the 28th minute.
But 19-year-old Pedri went past two defenders both lunging to stop an expected shot before equalizing with a composed low finish past goalkeeper Iñaki Peña nine minutes later.
Aubameyang’s header hit the crossbar in the first-half injury time but was in the right place to turn in a squared pass from Frenkie de Jong, who had collected the rebound after a good save by Peña.
Midfielder Mirko Ivanic gave Red Star some hope with a first-half goal before Ryan Kent’s deflected shot found the back of the net to restore a three-goal aggregate advantage for Rangers.
El FardouBen Nabouhane gave Red Star the consolation win on the night by converting a penalty in injury time.
Braga held a 2-0 advantage after the first leg and Abel Ruiz stretched it to three in Monaco before Axel Disasi equalized in the final minute.
Substitute Jeremie Boga scored the lone goal in second-half stoppage time to secure Atalanta’s 1-0 win at Leverkusen.
Leipzig advanced automatically as its opponent Spartak Moscow was among Russian clubs expelled from international competitions following the country’s military invasion of Ukraine.
EUROPA CONFERENCE LEAGUE
Leicester, the only English team in the last 16, had a 2-0 lead over Rennes from the first leg but the French club’s midfielder Benjamin Bourigeaud pulled a goal back early. Leicester defender Wesley Fofana headed in an equalizer off a corner kick in the second half in his first appearance of the season after seven months out with a broken leg.
Substitute Flavien Tait put Rennes back ahead in the 78th but the French club was denied a crucial third goal when goalkeeper Kasper Schmeichel pulled off a good save to stop Serhou Guirassy’s effort with five minutes left.
After a thrilling 4-4 home draw with Copenhagen in the first leg, PSV Eindhoven routed the Danish side 4-0 after two goals from Israeli forward Eran Zahavi.
Marseille came from a goal down to beat Basel 2-1 for a 4-2 aggregate score.
Norwegian champion Bodø/Glimt needed extra time to advance after a 2-1 win for AZ Alkmaar left the aggregate score tied at 3-3. Right-back Alfons Sampsted flicked in a low cross in the 105th minute to send the Norwegian side through.