LaRoche smacked a three-run homer in the first inning for a quick Washington lead and added a solo shot in the eighth.
In between, Tyler Moore and Roger Bernadina cracked back-to-back homers to put Washington ahead.
With the game tied 3-3 in the fourth, Moore belted an 0-2 pitch from Kevin Gausman into the Orioles bullpen for a two-run shot, and Bernadina followed with his first homer of year, a blast into the right-field stands.
Kurt Suzuki went 3-for-4 with a run scored for the Nats, who rebounded from a 6-2 loss Monday in the first contest of their four-game, home-and-home rivalry series with the Orioles.
Zach Duke (1-1) notched the decision with 1 2/3 innings of scoreless relief.
Gausman (0-2) was lit up for seven runs on eight hits over four full innings in his second major-league start for Baltimore.
J.J. Hardy went 3-for-4 with a solo homer and and Chris Davis added two hits, including a bases-empty clout, in the O's loss.