KANSAS CITY, Mo. -- Jake Odorizzi was having a miserable August but finished it with a victory.

Odorizzi picked up his first victory in six starts and Logan Morrison homered to continue his hot streak as the Tampa Bay Rays downed the Kansas City Royals 5-3 on Wednesday night.

Odorizzi (7-7), who was 0-3 with a 6.75 ERA in his first four August starts, allowed three runs and four hits, two that failed to leave the infield, in five-plus innings. He walked three, struck out three and posted his first victory since July 17.

"A lot of improvement over St. Louis to here," Odorizzi said. "I was more down in the zone tonight, better quality off-speed pitches. I'm going in the right direction. I just need to do it longer."

Morrison has 33 home runs and 76 RBIs, both career highs. His fifth-inning home run was his second of the series and the fourth in four games.

"I was impressed with the way Jake ended up throwing the ball," Rays manager Kevin Cash said. "He was very efficient with his pitches. He got on a nine-out groove once they scored three runs and that was good to see for Jake. It has not been easy for him."

Jason Vargas (14-9) was the losing pitcher, giving up five runs, seven hits and a walk in six innings. He fanned one.

"It's just frustrating because you know your capabilities of getting out of situations," Vargas said. "You know, put the other team in a good position to win the game and we were able to do such a good job of not letting that happen early in the season. So it's mental battles that you've got to overcome throughout the season. You push forward and get into September and hopefully things turn and we get on a nice roll."

Alex Colome picked up his big-league-leading 40th save, striking out three in the ninth, although he did give up a single to Salvador Perez.

The Rays (67-68) won the three-game series and moved a half-game above the Royals (65-67) in the American League wild-card standings.

"We'd be watching all day," Odorizzi said of watching the scoreboard for wild-card contenders. "There's so much that goes on with the wild card and how close things are right now for five or six other teams. It's almost too confusing to watch."

Vargas retired the Rays on seven pitches in the first inning. Morrison led off the Tampa Bay second and Vargas had to throw him 13 pitches before he flied out.

Vargas labored through a 27-pitch third inning, giving up three runs, three hits, a walk and a sacrifice fly.

With one out, Adeiny Hechavarria homered to left-center field, a 399-foot shot on a 1-0 Vargas pitch.

No. 9 hitter Peter Bourjos drew a walk and motored to third on Kevin Kiermaier's single to center. Steven Souza Jr. singled home Bourjos with Kiermaier taking third. Evan Longoria's flyout to center fielder Lorenzo Cain got Kiermaier home.

Odorizzi could not hold the lead long. He walked Cheslor Cuthbert to lead off the third and Alcides Escobar had a bunt single. Whit Merrifield drove an Odorizzi cutter out to left with Cuthbert and Escobar aboard, his 17th home run of the season.

"I made one pitch, a hanging slider and he put a good swing on it," Odorizzi said. "When we took the lead (again), I wasn't going to give it up again."

But that was it for the Kansas City offense, which got only one single against three Tampa Bay relievers after Odorizzi left.

"We had it cooking in the first inning," Royals manager Ned Yost said. "You think first and second, and Melky (Cabrera) lines to the shortstop who turns a double play right there. Outside of that, we just really didn't have too many scoring opportunities. Whit capitalized, first and second, with a three-run homer, but outside of that, not too much."

Souza and Morrison stroked solo blasts in the fifth to give the Rays a 5-3 advantage. Souza took a curve out to left, his 28th home run of the year. Morrison clobbered a Vargas 85 mph fastball out to right, his 33rd home run. The two shots covered 852 feet.

"I actually can do it, that's two home runs off a left-hander," Souza said.

NOTES: After a day off Thursday, the Royals have only one more off day the remainder of the season, on Sept. 18. They were to be off on Sept. 25, but instead will have a makeup game at the New York Yankees. ... With rosters expanding to 40 on Friday, don't expect the Royals to add any names that have not been with them earlier this season. The promotions will likely come in two waves, on Friday and on Tuesday after Triple-A Omaha's season ends. ... The Royals could also reinstate RHPs Joakim Soria, Neftali Feliz and Trevor Cahill soon from the disabled list. ... The Rays continue this trip with a three-game series beginning Friday at Chicago against the White Sox. Rays LHP Blake Snell (2-6, 4.29 ERA) will start the series opener. ... Royals RHP Jason Hammel will start Friday at Minnesota in the first game of a weekend series.