"Hopefully we can enjoy the moment and embrace it, have fun with it," he said.
They sure will if he keeps pitching the way he did Friday night.
"You could sense the energy out there, and it is a lot of fun to play in," first baseman Eric Hosmer said. "Huge win for us. We have to take the first game of every series -- that is the goal."
Kansas City (78-61), which opened a two-game lead over second-place Detroit in the AL Central, is in first place in September for the first time since 1985 -- when the Royals won the World Series in their last postseason trip. Kansas City has won four in a row and is 17 games over .500 for the first time since 1989, according to STATS.
Two starts after losing to the Yankees 8-1 in one of his worst outings this season, Shields (13-7) retired his first 11 batters before Brett Gardner's double in the fourth. Headley singled in the fifth, and Gardner flied out to the right-field warning track in the sixth.
Shields retired 11 straight before Derek Jeter singled softly with one out in the ninth.
"I think that is by far the best game he has thrown all year," Royals manager Ned Yost said. "He was surgical with his stuff. He had everything going, his curve, his changeup. He was spotting his fastball. He commanded the pitch count tremendously."
With closer Greg Holland bothered by triceps tightness, Yost brought in Wade Davis. After pinch-runner Antoan Richardson stole second, Gardner struck out swinging on a 98 mph full-count pitch. Carlos Beltran then took a called third strike, giving Davis his first big league save.
"He was up to the challenge," Yost said of Davis, who has fanned 92 batters in 62 1-3 innings this season.
New York rarely hit the ball hard against Shields, who induced 12 groundouts. He allowed three hits in 8 1-3 innings, struck out five, walked none and hit a batter with a pitch.
"He pitched way different than the Shields we faced in Kansas City," Beltran said. "Today he was using a lot of cutters and the changeup away. So basically he kept us off balance all game long."
New York began the night four games out for the second AL wild card and is in danger of missing the playoffs in consecutive years for the first time since 1992 and `93.
Michael Pineda (3-4), who has not allowed more than two runs in any of his 10 big league starts this year, has received 18 runs of offensive support in his last 13 outings dating to August 2013.
He was hurt by the Yankees' defense in the third, when Alcides Escobar hit a hard, one-out grounder that glanced off Headley's glove at third and into left field. Escobar hustled into second and scored an unearned run two pitches later when Aoki singled to center.
Pineda was nearly as sharp as Shields, giving up three hits, all singles, in seven innings with no walks.
"To win in New York, 1-0, that is one of the best games of our season," Escobar said.
Yankees: INF-OF Martin Prado, recovering from a left hamstring strain, was available to pinch hit but didn't play. He could be back in the starting lineup Saturday.
Yost doesn't bother to watch the scoreboard and see how his team's rivals are doing.
"Other people can do it. I don't like to do it. I like to just stay focused on what we're doing. I'll look at the standings every couple of days," he said. "I'm not up for staying up late and studying."
After the Royals arrived in New York on Thursday evening, he had dinner and didn't watch the Tigers-Indians game, won by Detroit 11-4 in 11 innings just before midnight.
"I was in bed way before that game ended," Yost said.
BATTING PRACTICE CHATTER
A different type of batter was speaking with Jeter on the field before the game: retired Indian cricket captain Sachin Tendulkar. The batsman is nicknamed the "God of Cricket."