Goalkeeper Maxime Crepeau needed to make just one save while earning the shutout in his LAFC debut.
Vela had five goals in 20 games during an injury-plagued 2021. He scored 34 goals in a single season for LAFC as recently as 2019.
Los Angeles is 5-0-0 in season openers since entering MLS in 2018. Colorado was shut out to start the campaign for the second straight year.
It was a slow start for both sides, with much of the play lingering around midfield in the opening minutes.
The Rapids had some sustained time in the attacking third around the 15th minute, but failed to get a shot on goal.
After a hand ball in the penalty area by Colorado's Lalas Abubakar, Vela converted on a penalty kick to give the home side a 1-0 lead in the 29th minute.
Vela struck again to make it 2-0 in the 35th minute. Midfielder Jose Cifuentes won a battle on the defensive side of midfield and found Vela with a long pass behind the Rapids defense. Vela managed to stay onside and struck from the area of the penalty spot with Abubakar draped on his back
The second Vela score appeared to deflate the Rapids, who struggled to muster any form of attack in the opening half, with just two shot attempts, neither of which reached the target.
LAFC had nine shot attempts in the first half, four of them on goal.
Vela completed his first hat trick since 2019 in the 50th minute, coming down the right side before cutting inside at the top of the box and curling a shot off his left foot that went into far side of goal past Colorado goalkeeper William Yarbrough, who had four saves.