The 33-year-old Wales international, who joined LAFC last month following the end of his nine-year stay at Real Madrid, secured the points seven minutes from time after Cristian Arango had opened the scoring for the visitors at Children's Mercy Park.
Bale's maiden strike came in trademark fashion as he cut inside from the right before firing home left-footed after being introduced with 25 minutes remaining.
He told the club's official website: "The most important thing was we won the game, first and foremost. We all knew the first half maybe wasn't good enough, but the manager had another great team talk and got us going.
"It was a great finish by Chicho (Arango) and it was nice to come on and grab a goal to help the team and to get the three points, so from a personal point of view, it's nice to get off the mark and more importantly, get the three points."
He made his debut for the club, who currently sit at the top of the MLS Western Conference, in a 2-1 win at Nashville last weekend.
Asked how he was settling in, he said: "The transition has been just kind of normal and what I expected. It's going to take some time - I would be in pre-season now in Europe, so I'm getting my fitness back up quickly.
"The club is doing an amazing job to kind of progress me and not pushing me too quick, so I'm starting to feel better and better each day as training goes on and I was glad to contribute tonight.
"I'm enjoying it here. Everybody at the club has made me feel very welcome very quickly and I feel very settled straight away, and I think any player will tell you if they feel happy and settled, they start to play their best football."