The former Leeds United man's first-half goal helped LA earn a 2-2 draw at the Philadelphia Union to extend their unbeaten run to eight games.
Vincent Nogueira put the Union ahead just four minutes into the match after taking advantage of a defensive mix-up, before Rogers levelled things up 11 minutes later following a fantastic team move.
After building out from the back, captain Robbie Keane delivered a pinpoint pass to fellow forward Giovani dos Santos, who held the ball up with two deft touches before teeing up the sprinting Rogers to provide the finish with a curling left-footed shot.
The in-form Dos Santos later helped give LA the lead two minutes after the break when he combined with Steven Gerrard to set up Mike Magee, but the visitors would have to settle for a point in the end after an error by goalkeeper Dan Kennedy allowed rookie right-back Keegan Rosenberry to score from close-range.
Nevertheless, after making six changes to the side that beat the New England Revolution 4-2 at home on Sunday, Galaxy head coach Bruce Arena was relatively pleased with the way his side performed on the night.
“We changed six players from our game on Sunday, so I give our guys credit to deal with the travel and getting the point and playing against an impressive team,” he told LAGalaxy.com after the match. “Overall, I think we have to be pleased to leave with a point.”
On Rogers’ goal, the former US national team boss added: “It was a real good goal; it was a great finish by Robbie [Rogers] and I thought [Mike] Magee’s goal was a good one.
“There was some combination play with Dos Santos and Gerrard, and Mike did well to finish. We scored two pretty good goals.”
Wednesday’s result at Talen Energy Stadium extends the Galaxy’s unbeaten streak to eight games and leaves them sitting third in the Western Conference, having taken 19 points from their opening 10 matches of the season with five wins, four draws and just one defeat.