Cleveland ? One big swing ended one bad losing streak and one brutal month for the Kansas City Royals.

Ken Harvey hit his first career grand slam, and Eli Marrero homered twice to back rookie Denny Bautista as the Royals snapped a nine-game losing streak with an 8-1 victory Saturday over the Cleveland Indians.

Harvey, an All-Star last season who struggled in the second half of 2004 and began this year in the minor leagues, connected in a five-run third off Cliff Lee (2-1) as the Royals won for the first time since beating the Indians on April 19.

“It’s good to see guys coming in and cheering,” Marrero said. “It’s been so long. It feels good to finally break this.”

Marrero homered after Harvey’s slam and added a two-run shot in the seventh for the Royals, who finished April at 6-18 — the AL’s worst record.

Bautista (2-1) limited the Indians to just one run and five hits in six-plus innings. The lanky right-hander is the first Kansas City starter to win since April 10, a span of 17 games.

“After last night, I said somebody has to stop this,” Bautista said. “I knew we had to go out and get a win, and I wanted to do it. I had one rough inning, but I got through that.”

Travis Hafner homered for Cleveland, which can’t string two good games together and ended April at 9-14 — the second straight season the Indians have opened poorly. They went 9-13 a year ago.

“It’s getting to the point where we can’t say it’s early anymore,” Indians right fielder Casey Blake said.

Kansas City's Ken Harvey celebrates after he hit a grand slam in the third inning against Cleveland. The Royals won, 8-1, Saturday in Cleveland, snapping a nine-game skid.

Lee, who didn’t allow a run in his previous 14 innings over two starts, gave up five earned runs and eight hits in five innings.

The left-hander’s scoreless streak came to a crashing halt at 16 innings, and in grand style as Harvey connected for his slam in the third. He barely was back in Kansas City’s dugout when Marrero’s homer put the Royals ahead 5-1.

David DeJesus walked leading off and went to third when Indians shortstop Alex Cora’s throw to second on a possible force play sailed into right for an error. After walking Mike Sweeney, Lee was visited on the mound by pitching coach Carl Willis.

Whatever advice Lee heard didn’t help him as Harvey, recalled Thursday from Triple-A Omaha, drove the next pitch over the wall in left to make it 4-1.

“I made a bad pitch to Harvey,” Lee said. “I was trying to go fastball in, and I left it out over the plate. He hit a home run, and there’s nothing I can do about it now.”

As the Indians were carefully working around Sweeney and then devising a game plan to face Harvey, he was making plans of his own.

“I knew they would pitch around Mike,” said Harvey, who is 6-for-14 since coming up. “I knew when the pitching coach went out there, he would try to get ahead of me. I was looking for something over the plate.”

Kansas City pitcher Denny Bautista throws to Cleveland's Travis Hafner. Bautista pitched six strong innings in the Royals' 8-1 victory Saturday over the Indians in Cleveland.

Two pitches later, Marrero connected, and the Royals were on their way to ending the fourth-longest losing streak in club history.

“No question, it’s a relief,” Royals manager Tony Pena said. “We needed this game. We needed to score early and get ahead, so we could relax a little.”

Kansas City’s biggest inning this season came one frame after it loaded the bases but failed to score off Lee.

“I was trying to stop them again, but I couldn’t,” Lee said.

The Royals took a 6-1 lead in the fifth on Matt Diaz’s RBI single, and tacked on two more in the seventh on Marrero’s second homer of the game and third this season.

Hafner opened the second with his first homer, pulling a 1-0 fastball from Bautista into the right-field seats. It was the first homer in 95 at-bats for Hafner, who hit a career-high 28 last season.

Three relievers blanked the Indians on one hit over the final three innings to finish the six-hitter.

Notes: Cleveland has 24 homers this season — 19 solo shots. … Marrero has two career multihomer games. He also hit two homers with St. Louis against San Diego on April 20, 2000. … Royals LHP Andrew Sisco pitched the seventh, extending his scoreless streak to 15 1-3 innings. The 6-foot-10 Sisco is the tallest player in Kansas City history. … Indians 3B Aaron Boone, batting just .123 and only .080 (2-for-25) at home, got the day off. … Cleveland’s weather hasn’t helped warm the Indians’ bats. The average temperature for the club’s first 10 home dates was 51 degrees.