Alan Pulido scored on a penalty kick in the 17th minute, and Sporting KC (5-9-5) took a 1-0 lead into halftime. Pulido has four goals in his last three matches after scoring just once in his previous 19 appearances.
LAFC (8-3-5) pulled even early in the second half when rookie defender Denil Maldonado took a pass from Mateusz Bogusz in the 48th minute and scored the first goal of his first career.
Vela scored for a fifth time this season, using a pass from Aaron Long in the 90th minute to help the defending MLS champions earn a much-needed victory. The three points pull LAFC into a tie with expansion team St. Louis City for the top spot in the Western Conference, one point in front of the idle Seattle Sounders.
John McCarthy had six saves for LAFC. Kendall McIntosh saved two shots for Sporting KC.
LAFC entered play 0-5-1 in its previous six matches in all competitions. The club had just three losses in its previous 26 matches. LAFC’s longest run without a victory came in 2021, when it had a 0-3-5 stretch.
Sporting KC had won four straight at home entering play after a 0-3-1 start.
LAFC lost by shutouts in four straight matches in all competitions coming into play. The club had failed to score in five of its last six matches after being shut out five times in its previous 67 matches in all competitions.
Sporting KC ended a three-match skid against LAFC with a 1-1 draw earlier this season in L.A.
LAFC returns home to host the Seattle Sounders on Wednesday. Sporting KC travels to play the Galaxy on Wednesday.