CLEVELAND -- There was nothing wrong with the Kansas City Royals that a well-pitched game couldn't cure.

Tuesday night they got one.

Right-hander Kris Medlen pitched six strong innings and Alex Rios homered to lead the Royals to a 2-0 victory over the Cleveland Indians at Progressive Field.

After giving up 35 runs in their previous four games, three of them losses, the Royals gave up no runs in this one.

"We just needed to stop the bleeding," said Kansas City manager Ned Yost. "We needed a good pitching performance. We needed to get to the bullpen in the seventh inning with a lead."

All that happened for the Royals on Tuesday.

In 6 1/3 scoreless innings, Medlen gave up five hits, with one walk and no strikeouts. Right-hander Greg Holland pitched the ninth inning to pick up his 31st save.

Cleveland threatened in the bottom of the ninth, with runners at first and second and nobody out. But Holland retired the next three batters in order to preserve the win.

It wasn't the slam-dunk save the Royals are used to seeing from Holland, who in his previous two appearances gave up six runs on six hits in 1 2/3 innings.

"His velocity is down a little, which is a concern, but he has that closer's mentality, and the heart of a lion," said Yost.

Indians right-hander Josh Tomlin (5-2) pitched well enough to win, but got no run support. Tomlin tossed his second complete game of the season, a four-hitter, with six strikeouts and no walks.

"He was so good. He commanded everything," said Cleveland manager Terry Francona.

Medlen (4-1) dominated Cleveland hitters from start to finish. The closest the Indians came to scoring was in the first inning, when shortstop Francisco Lindor doubled with one out. Medlen retired left fielder Michael Brantley on an infield popout. Designated hitter Carlos Santana walked. But right fielder Lonnie Chisenhall grounded out to Medlen to end the inning.

"He was able to get his fastball by our barrels. We didn't square up many," said Francona.

Through six innings, Medlen held the Indians scoreless on three hits, with Lindor being the only Indian to reach second base.

"He had a quick pace, and he was banging strikes down in the zone," said Yost of Medlen.

The Indians mounted a rally in the seventh inning. With one out, catcher Yan Gomes singled and went to second on a single by first baseman Chris Johnson.

Medlen was relieved by right-hander Ryan Madson, who promptly pulled the plug on that rally. Madson struck out center fielder Abraham Almonte and third baseman Giovanny Urshela to maintain Kansas City's 2-0 lead.

Kansas City took a 1-0 lead by scoring a gift run in the second inning. With two outs and nobody on base, third baseman Mike Moustakas hit a towering popup in foul territory, near home plate. Catcher Gomes lost the ball in the twilight, and no teammate could get there in time to catch it.

"It was at a crazy hour of the night," said Tomlin. "I saw Yan lose it, and I looked up, and I lost it. It's tough. You execute a pitch and you want to get an out."

Given a reprieve, Moustakas belted a double off the center-field wall.

Moustakas went to third on a wild pitch and he scored on a single to center by catcher Salvador Perez.

The Royals extended their lead to 2-0 in the fifth inning on a solo home run by right fielder Alex Rios down the left field line. The fireworks that are detonated when an Indians player homers were inadvertently shot off as Rios rounded the bases -- and the Progressive Field crowd booed.

"That caught me off guard," said Rios, of the surprise fireworks display. "At first I heard people screaming and I thought maybe they called it foul. But that was nice."

Medlen held the Indians scoreless on three hits through the first five innings.

NOTES: In the Royals' first 13 games in September, their team ERA was 6.46. That raised their season ERA from 3.53 to 3.80. ... DH Kendrys Morales has 101 RBIs, the most by a Royals player since Billy Butler had 107 in 2012. ... Indians SS Francisco Lindor leads major league rookies with a .309 batting average. He is third among American League rookies with 97 hits even though he's 12th among rookies in games played. ... Since 2013, the Indians have the best September record in the American League at 42-24.+