Bale fired in a low shot seven minutes from time to seal three points for LAFC, who remain four points clear at the top of the Western Conference standings.
Former Real Madrid star Bale had come off the bench as a second-half substitute before scoring his first goal since arriving in Major League Soccer earlier this month.
The Wales international launched the move which set up his goal, quickly releasing striker Cristian Arango with a pass from deep inside his own half.
Arango, who had scored LAFC's opener, held the ball up well and then rolled a pass into the path of Bale, who had sprinted up in support of the counter-attack.
Bale took his time before nonchalantly prodding his finish past Tim Melia in the Kansas City goal.
"Obviously I think the most important thing is that we won the game, first and foremost," said Bale. "Nice to come and grab a goal and help the team get the three points.
"From a personal point of view it's nice to get off the mark but more importantly get the three points.
"The transition's been what I expected. I'm getting my fitness back up pretty quickly, and the club's doing an amazing job to progress me and not push me too quick.
"I'm starting to feel better and better as training goes on, and glad to contribute tonight."
Elsewhere on Saturday, there was a successful debut for Toronto FC's high profile Italian signings Lorenzo Insigne and Federico Bernardeschi.
Bernardeschi scored and set up another in a 4-0 win for Toronto over Charlotte.
Standout matches today