Ibrahimovic claimed ahead of the match he was "by far" the better player between himself and Los Angeles FC's Vela.
And the 37-year-old backed up his words with actions by scoring the perfect hat trick -- right foot, left foot and a header -- to lead the Galaxy to a 3-2 win.
"Please do not offend me, I don't need to prove nothing, even if I don't score the goals today," Ibrahimovic told a postmatch news conference.
"I have a lot of respect for Vela, he's a good player, but you did one mistake, you compared him with me, that was your biggest mistake."
Vela opened the scoring early on before Ibrahimovic responded with three goals of his own. Vela's late strike took his tally to 21 for the season for MLS' leading scorer but it wasn't enough.
"I have my confidence and I believe in myself. People call it arrogant, I call it confidence. Ignorant people call it arrogant, intelligent people call it confidence," Ibrahimovic said.
"I have a bulletproof mind. When I go out there, I know what I'm able to prove -- and I do it good."
The victory cut LAFC's lead at the top of the Western Conference to nine points and Galaxy manager Guillermo Barros Schelotto was full of praise for his match-winner afterwards.
"He's wonderful. Not today, always," Schelotto said. "Today he was the best player on the field."
ESPN FC's Cesar Hernandez contributed to this report.