A stunning half-volley followed by a neat tap-in had Fernandes, and United, two goals to the good inside 20 minutes at Old Trafford.
After Basaksehir defender Boli Bolingoli had felled Rashford in the area, Fernandes was expected to wrap up a hat-trick in the first half, only for his team-mate to take the ball and convert.
Fernandes had scored from the spot against West Brom at the weekend and is recognised as United's first-choice penalty taker, but the Portuguese is a man of his word.
"Of course every player wants a hat-trick, but after the game in the Premier League I told Rashford that he could take the next one," Fernandes told BT Sport.
"Also, he's one of the top scorers in the Champions League so it's important for him to get the confidence.
"It doesn't matter who takes the penalty as long as the team scores."
Manager Ole Gunnar Solskjaer had no problem with Fernandes and Rashford sharing duties, adding: "Marcus is a very good penalty taker and Bruno is very confident, if Bruno wants to give it to Marcus then why not?
"Anthony Martial took one against Leipzig too - why not share it around?"