The Swedish superstar forward, who moved from Paris Saint Germain in the summer, was finally unleashed by new manager Jose Mourinho in Gothenburg in his native Sweden.
He had hardly broken sweat when, after just 190 seconds, Antonio Valencia — who was to grab three assists in all — swung over a deep cross and Ibrahimovic swung a right boot at it.
It was not the cleanest of volleys — and Mourinho barely acknowledged the goal — but it was enough to bounce into the ground and into the top corner to deceive Fernando Muslera in the Galatasaray goal.
The 34-year-old Ibrahimovic was replaced at the break, when Galatasaray led 2-1 through Sinan Gumus and Bruma.
Wayne Rooney scored a second-half brace and Marouane Fellaini and Juan Mata were also on the scoresheet as United came on strong after half-time.