Eyebrows were raised ahead of kickoff when Man United boss Erik ten Hag revealed that right-back Noussair Mazraoui would be playing in the number 10 position despite the likes of Amad Diallo and Antony being available.
However, Mazraoui was involved in Man United's breakthrough goal, with the Moroccan finding Joshua Zirkzee, who set up Eriksen, with the Denmark international firing one into the corner of the net to make it four goals this season.
Marcus Rashford came close to making it 2-0 shortly after, but his effort just missed the post, with Man United threatening on the counter-attack due to the pace of the Englishman and Alejandro Garnacho.
Manuel Ugarte produced a brilliant block to prevent Dusan Tadic from levelling the scores in the period that followed, before Man United goalkeeper Andre Onana made two stunning saves in quick succession late in the half to keep out En-Nesyri.
Fenerbahce were level early in the second half, though, with En-Nesyri heading a cross from Allan Saint-Maximin into the back of the net from close range, with Victor Lindelof and Lisandro Martinez unable to deny him.
Jose Mourinho was sent off just before the hour, with the Fenerbahce manager showing his frustration when the referee waved away a penalty appeal, as Bright Osayi-Samuel went down inside the box under minimal contact from Ugarte.
Both sides had their moments in the spell that followed, but neither were able to score for a second time, with the points ultimately being shared, which was the right result all things considered.
The result has left Man United in 21st spot in the Europa League table, boasting three points from three matches, while Fenerbahce are 14th, now on five points from their three European fixtures this term.
FENERBAHCE VS. MAN UNITED HIGHLIGHTS
Christian Eriksen goal vs. Fenerbahce (15th min, Fenerbahce 0-1 Man United)
Mazraoui the world-class number 10? The Moroccan is involved in Man United's opener, finding Zirkzee, who then delivers into Eriksen, and the midfielder expertly finds the corner to make it 1-0 to the visitors.
Excellent work from Ugarte and Garnacho in the build-up as well.
Andre Onana double save vs. Fenerbahce
Incredible goalkeeping from Onana, as the Man United stopper twice denies En-Nesyri in quick succession. Mourinho is absolutely flabbergasted that Fenerbahce have not levelled the scores here!
Youssef En-Nesyri goal vs. Man United (49th min, Fenerbahce 1-1 Man United)
Fenerbahce level the scores in the 49th minute of the contest, as En-Nesyri heads a cross from Saint-Maximin into the back of the net from inside the box. Not sure about the defending from the visitors there!
MAN OF THE MATCH - MANUEL UGARTE
Ugarte has had a tough start to his Man United career, but this was a standout performance from the midfielder.
The Uruguay international produced a stunning block in the first period to prevent a certain goal, while he was also heavily involved in Man United making the breakthrough in Turkey.
There have been questions asked about the 23-year-old in the early stages of his time at Old Trafford, but he showed his worth on Thursday evening with a dominant midfield performance, also completing 31 of his 35 passes in Istanbul.
FENERBAHCE VS. MAN UNITED MATCH STATS
Possession: Fenerbahce 52%-48% Man United
Shots: Fenerbahce 10-12 Man United
Shots on target: Fenerbahce 5-5 Man United
Corners: Fenerbahce 5-3 Man United
Fouls: Fenerbahce 12-14 Man United
WHAT NEXT?
Man United's attention will now switch back to the Premier League, with the Red Devils heading to West Ham United on Sunday afternoon; a total of 11 points from eight games has left Ten Hag's side in 12th spot in the Premier League table.
Fenerbahce, meanwhile, will resume their Super Lig season at home to Bodrum FK on Sunday afternoon; Mourinho's side are currently fourth in the Super Lig table, picking up 17 points from their opening eight matches, which has left them eight points off leaders Galatasaray.