Ibrahimovic, 34, met
Antonio Valencia's cross with a typically athletic volley as United beat Galatasaray 5-2.
The Turkish side bossed the remainder of the half and led thanks to goals from Sinan Gumus and Bruma.
But a much-changed United side turned the match around through Wayne Rooney (two), Marouane Fellaini and Juan Mata.
And Swedish striker Ibrahimovic believes the future is bright for the Red Devils, who continue to be linked with a £100m move for Juventus midfielder Paul Pogba.
"There is something big on the go, it's going to be very interesting this year," he said. "Let us say that if Pogba comes too, it's going to be very interesting.
"I'm going to help the team as much as I can and do what I'm good at, creating chances and scoring goals."
Manager Jose Mourinho used 22 players and will leave Gothenburg with as many questions as answers as he ponders his starting XI for next Sunday's Community Shield, which sees his FA Cup winners face Premier League champions Leicester at Wembley.
Ibrahimovic led the line in the first half, with Rooney behind him and Anthony Martial and Henrikh Mkhitaryan either side.
But half-time replacements Marcus Rashford, Ashley Young and Jesse Lingard looked far sharper and led to United's revival after a sleepy first 45 minutes.
Rooney equalised with a clean volley from another Valencia cross before Rashford won a penalty with an individual run from near halfway, and captain Rooney converted.
Valencia then made another goal as Fellaini drifted a header into the corner and Mata - who was sold by Mourinho at Chelsea - collected Michael Carrick's clever ball to slide in.
World Cup winner Bastian Schweinsteiger - one of nine players reportedly told they can leave the club - did not feature.
Manchester United manager Jose Mourinho:
"If the players 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.
"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."
Manchester United: De Gea, Valencia, Bailly, Blind, Shaw, Schneiderlin, Herrera, Mkhitaryan, Rooney, Martial, Ibrahimovic. Subs: Johnstone, Romero, Darmian, Jones, Rojo, Fellaini, Carrick, Lingard, Mata, Young, Memphis, Rashford.