WASHINGTON — Kenley Jansen, the Los Angeles Dodgers closer, was in the midst of the most exhausting outing of his career on Thursday. His right arm had already carried the weight of two innings as the Dodgers clung desperately to a one-run lead over the Washington Nationals in Game 5 of a National League division series.

As the Dodgers batted in the top of the ninth inning, Jansen was in the dugout tunnel when he caught of a glimpse on television of his teammate Clayton Kershaw, a starter, warming in the bullpen, a defining moment in an already extraordinary game.

“Wait a minute, am I dreaming right now?” Jansen said after the game. “I can’t believe it. Is Kershaw warming up? Is he really out there?”

He was. In this win-or-go-home game, Dodgers Manager Dave Roberts ripped up the book on conventional bullpen management. After Jansen could not complete the bottom of the ninth, Kershaw — two days removed from throwing 110 pitches on short rest — notched the final two outs in a wild 4-3 victory that sent the Dodgers to the N.L. Championship Series to face the Chicago Cubs.