United were knocked off their stride from the first whistle, with Sow's excellent effort inside just two minutes. Wayne Rooney and Zlatan Ibrahimovic came close, but their half was marred further by the loss of Paul Pogba.
It was a bright start for United in the second period, with chances from Rooney and Juan Mata but Jeremain Lens' strike before the hour mark look to have secured the points. Rooney got one back just before the end of the contest, but it only proved to be a consolation.
Right out of the top draw
However, the home support inside the Şükrü Saracoğlu Stadium erupted after just two minutes, as Fenerbahce took the lead in the most spectacular style.
The goal seemingly came from nothing as Hasan Ali Kaldirim played a ball in looking for Sow. The striker only had one thing on his mind, attempting the overhead kick just inside the area, and it paid off as it looped over David De Gea and in.
From bad to worse
United started to take control from there, with Rooney's heavy touch letting him down in the 21st minute after a wonderful through ball from Anthony Martial. However, it was about to get worse for Mourinho's side.
Pogba seemed to be suffering from an earlier knock but strode on determinedly. His efforts were in vain, though, forced to come off minutes after the initial contact, limping off just before the half-hour mark.
Ibrahimovic was brought on in his place and had a go just minutes after coming on. Marcus Rashford played a good ball over to the Swede at the back post in the 34th minute. It looked easy enough for Ibrahimovic to tap home but Volkan Demirel did well to get down and block the chance.
A brighter start
Mourinho's side came flying out of the traps in the second period and had good opportunities to get back into the match.
Rooney was a man in desperate need of a goal and came close in the 54th minute when he got on the end of Anthony Martial's cross, but his header flashed wide.
Martial was at it again four minutes later, when his cross was only cleared as far as Mata, but the Spaniards' effort again flashed past the post.
Out for the count
As United looked to be on the up, they were swiftly knocked down as Fenerbahce notched their second.
It seemed Advocaat's side weren't stopping there and substitute Emmanuel Emenike was on a mission to try and get the Turkish side's third.
It took him only a minute to get his first shot, Lens picking him out in the middle. He managed to get the shot off despite the pressure from Daley Blind, but De Gea did well to smother the ball.
He was it again 15 minutes from time, he tried an effort from 25 yards out, but once again De Gea did well to get down and save well.
To no avail
The Red Devils made it a nervy last few moments, as they managed to get one back a minute from time. Fans inside the Şükrü Saracoğlu Stadium were treated to a flurry of excellent goals, and Rooney's was no different. The striker decided to lash one from 25 yards, and it gave Demirel no chance as it nestled into the top corner. The skipper almost saved his side a point in stoppage time, he headed an effort towards goal but Ismail Koybasi did well to head it off the line.