The Portugal international scored two goals in a devastating first-half display that included a sublime strike for his opener.
The 26-year-old sent a perfect half-volley flying into the net after just nine minutes and followed it up with a simple finish to double his tally within 20 minutes.
However, the night could have been even better for Fernandes, who was handed a golden opportunity to complete his hat trick after the referee awarded the Turkish hosts a penalty.
United’s usual penalty-taker, who scored a spot-kick Saturday, looked set to take the penalty but opted to pass the ball to Marcus Rashford instead.
The England international dually obliged to put his side up 3-0 and went straight to Fernandes to celebrate.
“After the last Premier League game, I told (Rashford) he could take the next penalty, so I remembered that,” Fernandes told BT Sport after the match.
“Also, he is one of the top scorers in the Champions League. It’s important for him to keep going there and take that confidence. It doesn’t matter who takes. When the team scores, I score, too.”
Fernandes on fire
Fernandes has had a huge impact on Manchester United since joining at the start of the year, but few moments have been as impressive as the first goal.
He caught the shot perfectly after the ball was cleared from a corner and drilled it past keeper Mert Gunok from just outside of the area.
“It was a really good goal. I always say we need to be ready outside of the box to these kind of situations or sometimes to stop the counter,” he added.
“This time was to shoot — maybe next time I will have to foul and take a yellow card.”
His second was a little more fortunate after Gunok spilled a cross at the feet of the midfielder, who had the simple job of tapping it in.
Fernandes has now been involved in 34 goals in his 35 appearances — 21 goals and 13 assists — since moving to Old Trafford, according to the sports analytics firm Opta.
His influence was underlined after being taken off in the second half when the match was won.
United, which was so impressive going forward with Fernandes on the pitch, looked short of ideas in the second period as Basaksehir was allowed back into the game.
Second-half substitute Daniel James finally put the match to bed in stoppage time after Deniz Turuc scored a free kick to give the visitors a sense of hope.
United needs just one point for its next two group games to qualify for the knockout stages and faces last year’s beaten finalists Paris Saint-Germain next.
Busy night of action
Elsewhere, Juventus qualified for the last-16 of the Champions League after late drama in its game against Ferencvaros.
The visitors had taken a surprise lead in the first half through Myrto Uzuni, who cheekily used Cristiano Ronaldo’s iconic celebration.
Such a stunt backfired shortly afterward as Ronaldo equaled the scores with a long-range effort.
The hosts dominated the second period and finally found the winner as Alvaro Morata scored a stoppage-time header.
Meanwhile, Barcelona secured safe passage into the knockout stages after a comfortable 4-0 victory over Dynamo Kyiv.
A brace from Martin Braithwaite was bookended by goals from US star Sergino Dest and Antoine Griezmann.
Barcelona was without star man Lionel Messi after manager Ronald Koeman decided to rest a number of first-team regulars.