It marks just the second time in six matches that Western Conference-leading LAFC (19-8-4, 61 points) earned a point. LAFC lost four of its previous five matches.
Minnesota United had two major chances in the final two minutes before settling for a tie.
First, a long pass went downfield for Emanuel Reynoso and LAFC goalkeeper Maxime Crepeau came forward, but the ball took a high bounce over his head. Just as Reynoso got first touch on the ball, LAFC's Kellyn Acosta was able to knock it away before Reynoso could take a shot.
Then in the fifth and final minute of stoppage time, the Loons' Jonathan Gonzalez sent a header just wide of the net.
Reynoso, Minnesota's leading scorer, played the entire match after missing the team's previous game with an ankle injury.
Minnesota was outscored 7-0 during its three-game slide.
Dayne St. Clair made two saves for Minnesota, while Crepeau had one for LAFC.
The Loons had a 12-10 edge in shots. But LAFC held a 3-2 advantage in shots on target.
Kallman gave Minnesota a 1-0 lead in the 45th minute. Reynoso took a corner kick and sent a cross toward the net. Kallman rose up and headed the ball past Crepeau for his second goal of the MLS campaign.
LAFC evened the score in the 19th minute of the second half when Vela sent a hard left-footed blast from beyond the box into the left corner of the net for his ninth goal of the season.
Before Kallman's goal, both teams missed big chances in the first half.
Minnesota's Luis Amarilla hit the right post in the 21st minute, while Reynoso put a close-range shot just wide right in the 39th minute.
Vela chipped a shot over the net for LAFC in the 33rd minute, while Cristian Arango sent a close-range header left of the net in the 43rd minute.
Arango, who has a team-best 16 goals, was subbed out of the match at halftime.