Kansas City's Alex Gordon drives the ball to left field for an RBI double in the third inning. The Royals beat the Indians, 6-1, Sunday in Kansas City, Mo.

Kansas City's Mark Grudzielanek (15) celebrates his two-run, fifth-inning home run with teammate David DeJesus. The Royals beat the Indians, 6-1, Sunday in Kansas City, Mo.

Kansas City, Mo. ? Nothing restores the bounce to a ballplayer’s step like bringing a long losing streak to a halt.

Feeling refreshed after snapping a demoralizing 12-game skid the night before, the Kansas City Royals got solid pitching from Brian Bannister and home runs from Jose Guillen and Mark Grudzielanek to beat the Cleveland Indians, 6-1, Sunday.

“We were a lot more loose and had a lot more energy and just kind of played more freely,” said Alex Gordon, who had a two-run double in KC’s second win in two weeks.

“Having that (streak) off our backs really helps.”

Bannister (5-6) was working on a four-hit shutout when Grady Sizemore homered with one out in the eighth. Ramon Ramirez then got the last five outs.

“Basically, this is exactly the opposite of how I tried to pitch the last time (a 4-3 loss to Minnesota). With that streak on the line, I really wanted to end it,” Bannister said. “We were all putting pressure on ourselves to stop it. Today I was able to pitch the way I pitch.”

Guillen, who went into a tirade and called his teammates “babies” after they squandered a five-run lead and lost their 10th straight on Wednesday night, was 3-for-4 with two RBIs. He homered leading off the second against Paul Byrd and had an RBI single in the third.

Grudzielanek hit a two-run drive off Byrd to give the Royals, the major leagues’ weakest-hitting team, a 6-0 lead in the fifth.

The struggling Indians, the defending AL Central champs, have lost five straight series.

“You’ve got to keep coming out here and trust in the process that eventually things are going to turn your way,” manager Eric Wedge said. “As long as you keep working to have better at-bats, as long as you keep working to play better baseball, eventually it’s going to come back to you.”

During the long skid, the Royals had given up three grand slams, lost a five-run lead in the ninth, been no-hit and swept in consecutive four-game series.

“With that thing ending yesterday, it was just nice to go out there,” Bannister said. “I think everybody was relaxed today. Everybody was having fun. It showed up in the hitting. It showed up in the defense. It showed up in my control and my pitching.”

Byrd (2-5) went 4 1/3 innings and was charged with six runs and nine hits. He dropped to 0-5 in six road starts.

“We need to turn it around and I need to give my team a better performance,” Byrd said. “But you have to give credit to the Royals. They hit some good pitches. When I did make a mistake to Gordon, he made me pay for it.”

Bannister struck out four and walked one to earn his first win in four starts. All five of his victories have come in day games.

“Obviously, I have the gods of the day game with me right now,” he said with a grin. “I don’t have an explanation.”

Alberto Callaspo, the Royals’ fourth starting shortstop in four days, had a wild fifth inning.

He failed to pick up what appeared to be an easy double-play grounder, giving Cleveland a great opportunity with runners at first and second and nobody out. But after Bannister struck out Kelly Shoppach, Callaspo leaped to snare Sizemore’s liner and threw to second for the inning-ending double play.

“That was huge,” Bannister said. “I went up and gave him a hug.”

Notes: While going 12-15, the Indians batted only .218 in May. It was their lowest since August 1968 when they hit .208 and the worst in the majors since the New York Mets hit .217 in September 2003. … Tony Pena Jr., inserted at shortstop for defensive purposes starting the eighth, made a great play on Shoppach, diving to his right to stop a hard grounder and throwing to first from his knees on the grass. … Grudzielanek’s homer was his first in 172 at-bats dating to Sept. 24.