CLEVELAND -- The Kansas City Royals are headed home on a high note.

Wednesday's 6-3 win over the Cleveland Indians was significant on several fronts for the Royals. The victory gave Kansas City a 5-4 road trip in which it won four of its last six games. The Royals, who are off Thursday, finished May with a 15-13 record, their first winning mark in the month since 2000.

Kansas City, which took two of three in both Baltimore and Cleveland after losing two of three in New York to open the trip, is 16-11 on the road. The Royals are 18-14 since losing 12 straight from April 11-24.

"It's time to forget about the streak," Kansas City manager Ned Yost said. "We've played really good baseball from that point on and we're going to continue to get better."

"We played three good teams," said left fielder Alex Gordon, who had two hits and drove in a run. "Baltimore and Cleveland are at the top of their divisions. We're starting to play a little better. This road trip is definitely a positive."

Bruce Chen overcame a rocky second inning and the Royals scored their first five runs with two outs. Chen (4-5) held Cleveland scoreless after giving up three runs in the second. Gordon, Johnny Giavotella, Mike Moustakas, Jeff Francoeur and Brayan Pena each had run-scoring hits to help Kansas City rally from a 3-0 deficit.

Chen worked the first five innings before relievers Tim Collins, Aaron Crow, Jose Mijares and Jonathan Broxton pitched scoreless ball over the final four innings. Broxton worked a shaky ninth for his 11th save.

Broxton retired the first batter, but Shin-Soo Choo walked and Jason Kipnis singled. Asdrubal Cabrera walked to load the bases, but Jose Lopez hit into a game-ending double play.

Cleveland, which has lost five of six, fell to 4-11 against left-handed starters.

The Indians announced before the game that designated hitter Travis Hafner will have arthroscopic surgery on his right knee on Thursday and is expected to miss four to six weeks. Catchers Carlos Santana and Lou Marson and third baseman Jack Hannahan are also out with injuries.

Cleveland has an off-day Thursday, which is about the only good news manager Manny Acta has had in the last week.

"This was not a good series," he said. "The week continues to be rough for us. Pitching sets the tone, and we aren't setting the right one. The day off comes at a perfect time. We all need to go home and relax, and come back and play better baseball on Friday."

Chen, who improved to 6-3 against Cleveland, chuckled when asked if he had to grind out the victory.

"It was a battle," he said. "The bullpen did a great job. Once we got the lead, I couldn't let my teammates down. It was a total team win."

Jeanmar Gomez (3-4) gave up five runs in five innings. The Indians, who swept a three-game series from Detroit last week, lost all three games in Chicago over the weekend and dropped two of three against the Royals. Cleveland, which is off Thursday, fell out of first place in the AL Central for the first time since April 24 with Tuesday's loss.

Kansas City scored twice in the third on an RBI double by Moustakas and a run-scoring single by Francoeur. Gordon's run-scoring double and an RBI single by Giavotella put the Royals ahead in the fourth. Pena, who had three hits, added an RBI single in the fifth. The rallies in the fourth and fifth began with two outs and nobody on.

"That just shows you our offense right now," said Yost. "They keep getting after it even with nobody on and two outs. That's a good sign."

The Indians scored three times in the second on run-scoring singles by Casey Kotchman and Choo and an RBI fielder's choice by Luke Carlin.

Moustakas hit an RBI double in the third before Francoeur's single to left made it 3-2.

The Royals scored two more with two outs in the fourth, when Gordon doubled off the wall in left and Giavotella hit a single through the right side .

Billy Butler, the only starter without a hit, added an RBI groundout in the eighth.

The Royals, who lost their first 10 home games of the season, return to Kauffman Stadium for a series against Oakland on Friday. Kansas City is major-league worst 5-17 at home.

"We've got to figure that out," Gordon said. "We've been playing better on the road. It's just one of those things that will come over time. We're due for a good stretch at home."

Gomez gave up 10 hits.

Left-hander Scott Barnes, called up from Triple-A Columbus before the game, made his major league debut in the sixth. He walked two and hit a batter, but didn't allow a run.

Johnny Damon singled in the sixth for his 2,736th career hit, which moves him past Goose Goslin and into 54th place on the career list.

Cabrera played shortstop Wednesday and was 1 for 4 with a walk. He was the DH on Tuesday after missing four games with a strained hamstring.

Game notes
Royals INF Yuniesky Betancourt (sprained right ankle) could rejoin the team this weekend. He is on a rehab assignment at Triple-A Omaha and has been on the DL since May 2. ... Kansas City LHP Jonathan Sanchez (biceps tendinitis) will likely get at least one more rehab start at Omaha. He's been on the DL since May 8. ... Royals RHP Felipe Paulino faces the A's on Friday. The Indians host Minnesota and RHP Derek Lowe will face the Twins. ... Struggling Indians RHP Ubaldo Jimenez, who has been bothered by cramping in his left side, won't make his next start until Tuesday at Detroit. He's 5-4 with a 5.79 ERA in 10 starts. ... Marson (mouth bruise) missed his third straight game.