Substitute Cristian Dajome also scored his first goal since arriving in D.C. in a trade from Vancouver last month.
Mateusz Klich added his second of the season in D.C.'s largest margin of victory over LA since a 4-1 home win in June of 2008.
Tyler Miller made six saves to preserve his second consecutive shutout and fifth overall this season.
After conceding a league-worst 71 goals during the 2022 season -- a rate of more than two per match -- D.C. (5-5-4, 19 points) has allowed only 16 in the first 14 games of manager Wayne Rooney's first full season in charge.
The Galaxy (2-8-3, 9 points) nearly matched D.C. in total shots and had more efforts on target. But they had few chances of true quality as they sank to a second consecutive defeat overall and fourth in a row on the road.
Manager Gregg Vanney's LA squad has scored only one goal in its first seven away games.
That said, the Galaxy were well in the game until Benteke broke through in the 71st minute.
The former English Premier League forward thought he'd put D.C. in front four minutes earlier on an apparent goal that was ruled offside.
But there were no doubts about a simple tap-in after a bad giveaway from LA goalkeeper Jonathan Bond.
Lewis O'Brien pressured Bond after he received a backpass, and after the goalkeeper lost the ball in his own penalty area, Benteke was first to it and sent a composed finish past the 'keeper.
Two minutes later, Benteke set up Dajome on a sequence that began when Miller sent the ball long from his own box and LA's defense failed to clear.
Benteke deftly chested the ball down and looked left to play his fellow attacker in past the LA back line, and Dajome finished low past Bond.
Klich completed the scoring in the 80th minute when he took advantage of another mistake from Bond, reacting first to a spilled cross to finish from close range.