Alex Gordon led off the tenth with a homer off Darren O'Day to cap his eventful game in which he also doubled in three runs, was picked off at first base, made a great catch in left field and got hit in the neck with a pitch.
His homer put Kansas City up 6-5 and Mike Moustakas added a two-run shot off Brian Matusz to pad the lead.
The Orioles tried to rally in the bottom of the tenth, with pinch-hitter Delmon Young driving in a run with two outs and putting a second man on base, but Royals closer Greg Holland retired Nick Markakis on a grounder to end it.
Four of Kansas City's five wins in this postseason have come in extra innings.
"These games, we've played so many of them that we're kind of used to them a little bit," manager Ned Yost said. "And we still have a lot of confidence."
Game 2 is Saturday at 4:07 p.m. in Baltimore, when rookie pitcher Yordano Ventura will make his second postseason start for the Royals against Bud Norris.
On Friday, Orioles manager Buck Showalter declined to say who it would be before the ALCS opener against Kansas City, leading to speculation it would either be Wei-Yin Chen or Norris.
After the Orioles lost, playing past 12:45 a.m., Showalter announced his pitcher.
"Norris. He was home by 11:30. We kept him around like we might need him. So Bud will pitch tomorrow. He was trying to beat the traffic out," Showalter said. "I told him to check with me before he left. I said, 'You can shower at home. Just be standing by the door and beat the traffic out after the last pitch.'"
The last few innings were played in intermittent rain, and Showalter said the forecast called for more showers until a couple of hours before the late-afternoon start at Camden Yards.
On Friday night, Gordon was at the center of much of the action all game, so there was a sense of expectation when he came to the plate in the tenth, and he duldispatched a high pitch into the stands beyond right field.
"Gordy just has a lot of confidence in his abilities," Yost said. "He's a guy that can hit by a pitch and do exactly what he did, drive it out of the ballpark tonight, after getting hit in the neck. So it was a huge hit for us at that point."
As the ball soared over the wall, Orioles reliever O'Day flung his cap to the ground in frustration.
"I made a mistake and he got it," O'Day said. "You go up there and roll the dice. Sometimes you win, sometimes you lose."
It was Baltimore's first loss of the postseason after sweeping Detroit in the division series.
This best-of-seven series was billed as Kansas City's speed against Baltimore's power, but the Royals didn't steal a base and hit all of the game's three home runs.
"We know we're capable of hitting home runs," Gordon said. "We didn't do it during the regular season. But it doesn't really matter. This is the postseason and we're starting to swing the bats better now. It's good to see."
Kansas City established an early lead with a four-run third inning.
Alcides Escobar hit a rare homer off Chris Tillman into the left-field seats, and the Royals then loaded the bases with two singles and a walk to set up Gordon, whose broken-bat fly landed about four feet inside the right-field foul line and pushed the lead out to 4-0.
Baltimore got an RBI single from Adam Jones in the bottom half to make it 4-1, but a diving catch by Gordon prevented further damage.
A sacrifice fly by Butler in the fifth made it 5-1, but in the bottom of the frame the Orioles scored three-times to make it a one-run game. Nelson Cruz hit an RBI double before Ryan Flaherty delivered a two-out, two-run single.
Kansas City starter James Shields made it out of the inning, but did not return after giving up four runs and 10 hits.
The rain that was expected for much of the day finally made an appearance in the sixth, shortly before Baltimore tied the game against the usually reliable Kansas City bullpen. The tying run scored off Kelvin Herrera on a low popup by Alejandro De Aza that dropped behind the mound.
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