After both teams put on a display of dominant pitching, the Los Angeles Dodgers outlasted the San Francisco Giants, 2-1, to win Game 5 of this division series and advance to the National League Championship Series against Atlanta.

The tense affair between these longtime rivals, each of which came into the game with 109 wins between the regular season and the postseason, came down to its final inning when Cody Bellinger, a former Most Valuable Player Award winner who struggled badly this season, shot a single into right, scoring Justin Turner from second.

Max Scherzer, a superstar starting pitcher, came in for the bottom of the ninth inning, earning a crucial save for a club he joined in July. It was the first save of his major league career.

The game was expected to be a premium pitching matchup between Logan Webb of the Giants vs. Julio Urias of the Dodgers. That got off to a strange start when Dodgers Manager Dave Roberts — looking to force the Giants not to stack up right-handed hitters against the left-handed Urias — chose to begin the game with Corey Knebel as an opener.

But the matchup materialized anyway, with Webb throwing seven strong innings, allowing one run, and Urias throwing four innings in relief, also allowing one. In the end it was Camilo Doval, the Giants’ 24-year-old closer, who allowed the decisive run.

This was the first postseason matchup between the rival clubs since 1889, when the Dodgers (then located in Brooklyn and known as the Bridegrooms) were champions of the American Association and the Giants (then located in Manhattan), who were champions of the National League, met in a precursor to the modern World Series. The Giants won that series, six games to three.

The N.L.C.S. is scheduled to begin Saturday in Atlanta.