Vela scored and set up two others as Supporter's Shield leader LAFC overcame the Red Bulls in a six-goal thriller on Monday (AEST).
The Mexico international took his season tally to 23 goals and 15 assists – matching Sebastian Giovinco's feat with 10 matches remaining in the regular season.
Vela teed up Jordan Harvey for the 23rd-minute opener before Latif Blessing doubled LAFC's lead two minutes later, however, the Red Bulls rallied from 2-0 down to level in a stunning end to the first half.
Ex-Real Sociedad winger Vela converted a penalty just past the hour to put him on track to eclipse Martinez's single-season record of 31 goals set last term.
Vela then assisted Eddie Segura 18 minutes from the end as LAFC won their third successive game to move 16 points clear of Seattle Sounders in the Western Conference and 10 ahead of Philadelphia Union in the race for the Supporters' Shield.
Meanwhile, Martinez broke an MLS record by scoring in a 10th consecutive game for Atlanta – who edged New York City 2-1.
Reigning Golden Boot winner Martinez made history with his 42nd-minute header at Mercedes-Benz Stadium, where the Venezuelan also scored from the penalty spot in the second half.
Heber pulled a goal back for visiting New York, however, defending champions Atlanta were not to be denied as they consolidated second spot in the Eastern Conference.
Zlatan Ibrahimovic attempted 15 shots – the most a player has taken in an MLS game this decade – as LA Galaxy lost 2-1 to a Wayne Rooney-less DC United.
In Monday's (AEST) other match, the high-flying Union was too good for Houston Dynamo 2-1.