Ibrahimovic opened the scoring in the opening moments in his homeland; however, United fell behind before the interval after goals from Sinan Gumus and Bruma.
It did not take the former Paris Saint-Germain striker long to get off the mark for his new club, as he scuffed an overhead kick into the ground and into the bottom corner inside four minutes.
Antonio Valencia was the provider who chipped a cross toward the penalty spot over the head of Rooney. Fortunately, Ibrahimovic was on hand to divert the ball on target.
MUTV provided footage of the Swede's first goal in United colours on their official Twitter account:
With 22 minutes on the clock, Galatasaray pulled level through a set piece. After Ibrahimovic conceded a sloppy free-kick 30 yards from goal, Wesley Sneijder whipped the ball into the area toward Gumus, who stabbed a header into the bottom corner and under Spain No. 1 David De Gea.
The Istanbul club moved ahead of their Premier League opponents five minutes before the half-time interval following a lovely flowing move. Portuguese midfielder Bruma darted inside from the left flank before letting fly with a powerful drive that flew into the corner of the net.
Manchester Evening News' Rob Dawson listed the substitutions for United, who made wholesale changes at the break:
However, 10 minutes into the second half, United were level. Valencia was once more the architect down the right wing, as the Ecuadorian played a neat one-two with Ashley Young before darting to the byline.
The experienced winger clipped an accurate ball into the six-yard box for Rooney to head over the goal line.
Dawson believed the manager Mourinho will have been impressed by Valencia's contribution:
United looked a transformed side after their 15-minute breather; moments later, Mourinho’s men were ahead. Eighteen-year-old striker Marcus Rashford was sent clear of the Turks’ back line and burst into the box before being brought down inside the six-yard box by goalkeeper Fernando Muslera.
Rooney took over responsibilities for the spot-kick, and despite a poorly struck effort, the ball found its way past the Uruguayan stopper.
Rashford's devastating pace could play a key role in Mourinho's future plans, according to Manchester Evening News' reporter Samuel Luckhurst:
In the 62nd minute, United added their fourth goal of the night. A deep ball from Valencia from the right of midfield found Belgium international Fellaini at the back post.
The former Everton midfielder’s domineering presence in the box paid off, as his looping header dropped under the crossbar to net United’s third goal in seven minutes.
With 15 minutes remaining in the contest, Mata added a fourth goal of the half to move United comfortably clear of their opponents at 5-2. The Spaniard linked well with Michael Carrick on the edge of the box before sprinting inside and collecting a low cross into the area, toe-poking the ball along the ground and into the corner of the net.
Sports journalist Liam Canning has high hopes for Mata ahead of the new campaign:
After further changes to United's line-up, including Sergio Romero coming on for De Gea, the game began to become slightly fragmented, with Galatasaray enjoying more of the ball than they had become accustomed to in the second period. However, they were unable to turn over the significant deficit, as United came from behind to win in their final pre-season of the 2016 tour.
Mourinho was forced to answer questions regarding his squad selection in the aftermath of his team's comeback victory over Galatasaray, with the Portuguese coach highlighting the importance of rotation ahead of a long campaign. Per MUTV (h/t Luckhurst of Manchester Evening News), he said:
If they were not in my plans I would not give them one single minute, I would not keep them in my squad. The squad is very competitive, the squad is very important for the season. We have 38 matches in the Premier League, we have the possibility of 15 matches in the Europa League, plus domestic cups, we are going to play 60 matches. So with 60 matches we cannot do it with 11 players.
So to be in the squad you have to understand that the squad is more important than the individual, the club is more important than all of us, and to be in the squad you have to be ready for this, to play, not to play, play a lot, play less, play 90 minutes, play one minute, not be selected, everything is part of a squad life. And if you want to be in a club like we are, the club is much more important than us.