Flaherty pitched seven scoreless innings as the Dodgers' shutout streak extended to 33 innings, tying the postseason record.
The Dodgers grabbed a 1-0 series lead with their 9-0 victory over the Mets on Sunday.
Left-hander Carlos Rodón will start Game 1 of the ALCS for the New York Yankees, and Gerrit Cole will get the Game 2 nod.
Game 1 of the ALCS will be Monday at Yankee Stadium.