The Nationals held a 1-0 lead after four innings when the contest was halted for 1 hour, 17 minutes by rain. When play resumed, the Giants tallied a score-tying run when shortstop Ian Desmond's error allowed Joaquin Arias to score on a Buster Posey grounder.
But the Nats responded in the sixth when Desmond (3-for-4, two runs scored) led off with a single and LaRoche followed by golfing a pitch from Guillermo Moscoso (1-1) deep over the right-field fence for a two-run homer.
Tanner Roark (2-0) notched the decision and Rafael Soriano picked up his 30th save for Washington, which took the opener of a three-game series.
Arias finished 4-for-5 with two runs scored and Hunter Pence supplied an RBI for San Francisco.