The 36-year-old, who only arrived from Manchester United last week, came off the bench with 71 minutes played to rescue his new side all three points.
Galaxy were 3-1 down at the time, having earlier trailed by three goals, but Chris Pontius pulled another one back and Ibrahimovic then took over.
Ibra's first strike, maintaining his incredible run of scoring on his debut wherever he plays, was a 40-yard volley that flew into the back of the net.
With normal time up the ex-Sweden international, who reportedly took a huge pay cut to join Galaxy, completed the turnaround by heading home what would prove to be the winner.
Speaking to reporters at full time, Ibrahimovic said: "They were saying 'We want Zlatan. We want Zlatan.' So I gave them Zlatan."
LA Galaxy are now second in the Western Conference, three points behind Vancouver Whitecaps who have played a game more.