Vela struck twice within six first-half minutes, first from the penalty spot before getting in behind the Colorado defence and calmly finishing past goalkeeper William Yarbrough.
The former Mexico international produced his best goal of the game to complete his hat-trick in the 50th minute, curling in a fine left-footed shot from just inside the box.
Vela only managed five goals from 20 MLS appearances last season with LAFC head coach Steve Cherundolo cautiously optimistic about his potential impact this term.
“We will have to wait and see what it does. But I think we all know what he can do,” Cherundolo said. “He showed it again today and he worked very hard in preseason to get to where he is today. I'm very happy for him and the group that we're all rewarded for it.”
Yimmi Chara's spectacular 78th-minute goal earned Portland Timbers a 2-2 draw with 2021 Supporters' Shield winners New England Revolution.
Portland, who reached the MLS Cup final last year, found a way back with Chara firing home a stunning overhead goal while Jozy Altidore debuted for the Revs as a 79th-minute substitute.
Ex-Liverpool and Bayern Munich midfielder Xherdan Shaqiri made his debut for Chicago Fire as they drew a blank in a 0-0 draw at Inter Miami.
Leonardo Campana's 10th-minute header from Gonzalo Higuain's cross hit the crossbar for Miami, while Chicago's Stanislav Ivanov struck the upright in the 31st minute. Shaqiri was impressive throughout, with a long-range first-half chance his only major goal attempt.
Toronto, who made a major off-season signing with Lorenzo Insigne to join in July, only managed a 1-1 draw at Dallas.
Philadelphia Union started its new season with a 1-1 home draw against Minnesota United, with Cory Burke levelling Robin Lod's 23rd-minute strike.
New York Red Bulls won 3-1 at San Jose Earthquakes, while Columbus Crew swept aside 10-man Vancouver Whitecaps 4-0.
Cecilio Dominguez netted a double as Austin won 5-0 over last year's bottom side Cincinnati, while Michael Estrada scored a brace as DC United eased past newcomers Charlotte 3-0.
Goals in the second half from Carlos Vela and Jose Cifuentes handed LAFC the three points, to put them three points clear of Austin FC, who have a game in hand.
James Igbekeme missed from close range for the Crew in the third minute and with the majority of possession, failed to create anything of substance from that point.
LAFC were able to punish them in transition through Vela in the 62nd minute, darting in behind the defensive line before finishing past Eloy Room.
Cifuentes doubled the margin in the 73rd minute, left with a relatively simple finish after Cristian Arango claimed the ball just outside the penalty area in a comical loss of possession from a Crew goal kick.
The win moves LAFC to 26 points from 13 games but elsewhere in the Western Conference, Nashville SC were unable to move to fourth, twice letting the lead slip in a 2-2 draw with Atlanta United.
In the Eastern Conference, DC United and Toronto FC also played out a 2-2 draw, while Tommy McNamara's spectacular finish in the 89th minute handed the New England Revolution a 3-2 win over Cincinnati.
The ex-attacker is set to move to a new role in Harrison as Special Assistant to the Sporting Director, after two seasons with Los Angeles FC and Columbus Crew respectively.
After confirming his retirement this week, the two-time Golden Boot winner has now officially signed off with the side he helped fire to a hat-trick of Supporters' Shield triumphs over a seven-year stint.
"It wouldn’t have felt right retiring somewhere else, especially in America, it wouldn’t have felt right," Wright-Phillips said in a statement. "I am honoured to get the opportunity to retire here, it means a lot to me."
Sporting Director Denis Hamlett, who Wright-Phillips will link up with, paid further tribute, adding: "There was no question in our minds to bring Brad back to the club following his retirement.
"The expansive experience that Brad brings from the field will be helpful in the development with our young players, while at the same time, Brad getting crucial experience on the sporting side for his own professional development."
Having broken through alongside brother Shaun at Manchester City, Wright-Phillips spent several seasons in the second and third tiers of English football, claiming the League One crown with Charlton Athletic in 2011-2012.
But it was in MLS where he made his name, joining the Red Bulls ahead of the 2013 season and helping to establish them as regular contenders.
He still holds the record for the most goals at the club, with 125, and won the Supporters' Shield on three occasions, in 2013, 2015 and 2018.
The bizarre incident occurred in stoppage time with the Red Bulls trailing 2-0 after Yearwood conceded a foul near the sideline, with the Englishman kicking away the ball in frustration.
Yearwood's errant kick cannoned into two young fans in the front few rows at Red Bull Arena, with a boy seen crying afterwards while a young woman seemed dazed. Yearwood immediately realised his error and attempted to apologise to the fans, by climbing into the stands but that effort was not accepted by those close to the shaken-up supporters.
The Red Bulls crowd could be overheard chanting against Yearwood before referee Timothy Ford gave him his marching orders.
The incident capped a poor night for the home side, with goals from Mikael Uhre and Daniel Gazdag clinching the win for Union, who sit top of the Eastern Conference.
Gazdag's goal, which came after Julian Carranza dispossessed Aaron Long, was his 18th of the campaign.
Dallas scored three goals in three minutes as Dallas firmed up their grip on a playoffs spot with a 3-0 road win over Minnesota United.
Michael Boxall netted a 55th-minute own goal before Alan Velasco curled in a right-foot strike less than a minute later.
Two minutes later, Velasco cannoned an effort into the crossbar with Jesus Ferreira glancing home their third after Sebastian Lletget collected the rebound and whipped in a cross.
Franco Fragapane was sent off for Minnesota, who also lost Emanuel Reynoso to a worrying ankle concern.
Cincinnati extended their unbeaten run to seven games and moved into the playoffs spots in the Eastern Conference with a 2-0 home win over Charlotte after goals from Nick Hagglund and Luciano Acosta.
Hany Mukhtar scored a double as Nashville claimed their fourth straight win and moved up to fourth in the west with an impressive 4-0 victory over Austin.
Columbus Crew missed a golden opportunity for three points with a 0-0 draw against struggling Chicago Fire.
