Kansas City, Mo. ? Kansas City’s best hitters failed to come through, so rookie Ken Harvey bailed them out.

Harvey homered leading off the bottom of the 11th inning and Kansas City handed the Detroit Tigers their 14th loss in 15 games this year, 4-3, Friday night.

“This clubhouse, everyone is jumping around like little kids,” manager Tony Pena said. “It’s good to see how much they care about each other. They waited for Harvey at home plate because they know he has been struggling, and he’s better than that.”

The Royals wasted a great chance to win in the 10th, loading the bases with none out against Matt Anderson for their 3-4-5 hitters. But Carlos Beltran, just off the disabled list, grounded into a force play at the plate, Mike Sweeney fouled out and Raul Ibanez lined out to center.

One inning later, Harvey made sure it didn’t matter.

He connected on an 0-2 pitch from Anderson (0-1) for his second home run of the season, sending a near-sellout crowd home happy.

“Harvey has been struggling,” Pena said. “I gave him the day off yesterday, just to see the game and get refreshed. He came through big for us.”

Ibanez homered to tie it at 3 in the sixth for the surprising Royals, who have won 12 of their first 15 games for the first time in team history.

After falling behind in the count, Harvey was just looking to put the ball in play. He did much more than that.

“I didn’t feel much pressure, because I was leading off the inning,” Harvey said. “My mind-set was just to get on base. I was not trying to hit a home run. I’m just glad I put a good swing on it.”

D.J. Carrasco (1-0) pitched two innings for his first major-league win. He got pinch-hitter Dmitri Young on a grounder with runners at the corners to end the 10th.

Pena wondered if Carrasco’s effort would be wasted, after the blown opportunity in the bottom of the 10th.

“You start thinking, ‘Uh oh.’ Of course, you don’t want to let the players see you make an expression,” he said. “But of course you think about it. That’s going to happen. But we went back for another inning and Carrasco gave Ken Harvey the chance to win the game.”

Anderson gave up three hits in one-plus inning.

“Obviously, we were down (after the 10th),” Harvey said. “I’ve been on a lot of teams where guys get down in that situation. We were kind of quiet, but it was a quiet confidence that we were going to get another chance.

“I’m proud of myself. I’ve had a pretty (lousy) week. I got down on myself a little bit, but I didn’t really show it like young guys do. I just tried to stay as positive as I could.”

The attendance of 38,937 was the Royals’ largest April non-opening day crowd since April 30, 1989, when 40,113 fans saw Kansas City play Milwaukee.

“They cannot ask for a better game,” Pena said. “It’s nice to see that they are starting to believe that we can win.”

Detroit starter Nate Cornejo, a Wellington native, allowed the first batter to reach base in each of the first six innings. But he managed to wiggle out of most of the jams. He pitched seven innings, allowing three runs, two earned, and six hits.

“We try not to think about (our record),” Cornejo said. “We know we’re struggling right now. We need to come together and keep going out there and battling every day. Sooner or later things will fall into place.”

Kansas City starter Darrell May gave up three runs, two earned, and seven hits in six innings.

“He did struggle a little bit, but he gave us what we asked for,” Pena said. “He kept us in the ballgame.”

The Tigers took a 2-0 lead in the third inning, when Bobby Higginson led off with his first home run of the season. Ramon Santiago walked, stole second and scored on Craig Monroe’s single to center.

The Tigers added an unearned run in the fourth when Gene Kingsale scored on an error by shortstop Angel Berroa.

The Royals answered with a run in the bottom half when Joe Randa led off with a double and scored on Sweeney’s RBI groundout. They got an unearned run in the fifth and tied it on Ibanez’s fourth homer.

Notes: It was the first extra-inning game for either team this season. … Higginson kept his average at .333 when batting leadoff. He went 2-for-6 and is hitting .107 (3-for-28) when batting elsewhere in the lineup. … The Tigers matched their largest lead of the season at 3-0 in the fourth. They led the Chicago White Sox by three runs in their lone victory, 4-3 on April 12.