The 36-year-old marked his arrival in the MLS by coming off the bench to score a pair of stunning goals as Galaxy came from 3-0 down to win 4-3.
However, he went one goal better on Sunday night, scoring a hat-trick in another entertaining encounter.
Orlando took the lead on three occasions in LA but they were pegged back on each occasion.
Ibrahimovic came up with an assist for the first Galaxy goal, nodding the ball to Giovani dos Santos, who conjured up a great finish.
Having levelled the score at 2-2 with a fairly routine header, Ibrahimovic made it 3-3 with a brilliant diving effort.
The striker completed his hat-trick when he controlled a cross at the back post and calmly volleyed the ball into the net to make it 4-3. That is 15 goals in 14 Galaxy starts for the Swede.