The 34-year-old former Barcelona, AC Milan and Paris Saint-Germain striker netted with a well-taken scissor kick from an Antonio Valencia cross in a first half that saw the Turkish side score twice before a second-half United resurgence.
Red Devils boss Jose Mourinho rang the changes at the break with Wayne Rooney (two goals), Marouane Fellaini and Juan Mata cancelling out first-half strikes from Sinan Gumus and Bruma.
Ibrahimovic feels that with a £100m deal for Juventus midfielder Paul Pogba also potentially on the cards, the future is looking bright for his new team.
He told the BBC: "There is something big on the go, it's going to be very interesting this year. Let us say that if Pogba comes too, it's going to be very interesting."
Ibrahimovic added that he intends to work hard this season, and do what he does best: "I'm going to help the team as much as I can and do what I'm good at, creating chances and scoring goals."