Clayton Kershaw took the mound in the eighth inning, giving up back-to-back home runs that helped smother the Dodgers' bid for a fourth straight appearance in the National League Championship Series.
Kenta Maeda and Joe Kelly took the mound in following innings but the damage was done.
Both teams failed to bring in any more runs to break the 3-3 game until the 10th inning with a series-winning grand slam.
The end of the game was a stark contrast to the first six innings.
Max Muncy put the Dodgers ahead with a two-run blast in the bottom of the first, one batter after Joc Pederson hit a leadoff double that came close to leaving the ballpark. Pederson's drive originally was called a home run before being changed to a two-bagger upon video review.
Kike Hernandez added a second-inning blast off Nationals starter Stephen Strasburg.
Pederson had two of the Dodgers' first five hits allowed by Strasburg.
Dodgers starter Walker Buehler limited the Nats to two hits over the first five frames. Buehler put the first two runners on base in the top of the fifth before getting out of the jam unscathed.
Breaths were held at the beginning of the seventh inning after Buehler's 94-mph fast ball ricocheted off the National's Kurt Suzuki's left wrist and knocked his helmet off.
The Nationals are now moving on to face the Cardinals in a best-of-seven series beginning Friday. It will be St. Louis' first NLCS trip since 2014.
The Associated Press contributed to this report.