Nationals left fielder Juan Soto blasted a two-run home run off Dodgers starting pitcher Hyun-Jin Ryu in the first inning to give Washington a quick 2-0 advantage.
Dodgers first baseman Max Muncy belted a solo homer off Nationals starter Anibal Sanchez in the fifth inning before Los Angeles exploded for seven runs in the sixth to grab a commanding 8-2 lead.
Sanchez, who allowed one earned run on four hits across five innings, was replaced by left-hander Patrick Corbin, who hadn't made a relief appearance since 2017, in the sixth.
Russell Martin and Kike Hernandez each had RBI doubles and Justin Turner added a three-run blast as the Dodgers roughed up Corbin for six earned runs. Los Angeles became the first team in MLB history to score that many runs in one postseason inning with two outs and two strikes.
The Nationals mustered two more runs in the bottom of the sixth but couldn't generate any more offense late in the game. Martin tacked on a two-run homer in the ninth to seal the victory.
The Dodgers can advance to the NL Championship Series for the fourth straight year by closing the best-of-five series in Game 4 at Washington on Monday. Los Angeles will send Rich Hill to the mound against Nationals ace Max Scherzer.