They also unleashed thunderous cheers when Dyson scored to break the 1-1 deadlock in the sixth inning, and when closer Greg Holland recorded the final out of a combined three-hitter for the Royals, who shut down the last 16 Orioles batters. The Royals have a tangible momentum, as their undefeated record shows, and the city of Kansas City is ecstatic.

“We’re rolling as a team right now,” said first baseman Eric Hosmer, who also made a fine defensive play. “Stuff is going our way. People are making tremendous plays defensively, pitchers are getting it done, bullpen is getting it done. Everybody on the team is getting it done.”

This is a team that was trailing by four runs entering the eighth inning of the wild-card game against the Oakland Athletics, only to come back and win in 12 innings. The Royals went on to win three of their next four games in extra innings and then won Game 2 of this series by scoring two runs in the ninth.

It had been 29 years and one day since the A.L.C.S. was played in Kansas City between the Royals and the Toronto Blue Jays. But the Royals are making up for that long absence with an enthralling October. Tuesday’s game, delayed 24 hours because of heavy rains Monday, brought the Royals to within a game of their first World Series since the 1985 championship.

“We have a chance to do something pretty special here,” Hosmer said, “especially in a city that’s been dying for it for a very long time now.”

The Royals took the lead in the sixth when Dyson scored from third base on a sacrifice fly from Billy Butler. Nori Aoki had led off the inning with a single against Wei-Yin Chen and was replaced by Dyson, the Royals speedster who declared after Game 2 that he did not think the series would go back to Baltimore.

The Orioles took a 1-0 lead in the second off Jeremy Guthrie, the former Oriole, when Steve Pearce and J. J. Hardy both doubled. The Royals tied the score in the fourth when Lorenzo Cain and Hosmer singled back to back with one out and Butler walked to load the bases. Alex Gordon bounced a ball to the right side for an out, but Cain scored.