Davis stopped his five-game winless streak, Jeff Francoeur homered, and the Royals beat the Rays 5-3 on Sunday.
The Royals have given up three runs or fewer in 14 of 15 games. Kansas City has won 10 of 12.
"Kansas City is playing really well now," Rays manager Joe Maddon said. "They deserved to win. They're playing with a lot of confidence. If you look at their team ERA, it's number one in baseball. Kansas City outplayed us, period."
After the game, the Rays announced that they were going to purchase the contract of slugging prospect Wil Myers from Triple-A Durham in time for Tuesday's doubleheader at Boston. The outfielder, who hit 14 homers with Durham, was acquired in a seven-player offseason deal with the Royals that sent Davis and starting pitcher James Shields to Kansas City
Davis (4-5) gave up two runs -- both coming in the first -- and five hits in six innings for his first win since he beat the Los Angeles Angels on May 15.
"I knew once he got through the first, he was going to settle in and be fine," Kansas City manager Ned Yost said. "Wade did a great job of limiting the damage. I just had a real good feeling he'd get back in the dugout, he'd regroup and hold them right there. That's exactly what he did."
It was Davis' first game against the Rays.
"I was up in the zone a little bit," Davis said. "The walks and a couple of hits that got in there were just balls I left up a little bit. Once I got the breather in the third or fourth inning when we scored some runs, I got a little breathing room."
Francoeur had only 13 hits in 83 at-bats before delivering his third homer this season.
Roberto Hernandez (4-7) allowed four runs and nine hits in 5 2/3 innings for Tampa Bay, which went 4-6 on a 10-game homestand. The Rays were coming off a three-game series with Boston that included a 10-8 loss in 14 innings, and a 2-1 defeat.
"The Red Sox series was kind of a weird one," Rays third baseman Kelly Johnson said. "It was tough to lose a couple of those games. We had opportunities to win both. Then this series was one of those hangover series from that. It kind of felt that way anyway. Not a ton of energy, not a ton of life, unfortunately.
"There's always going to be some stuff like that. We've got to get it turned around quickly."
Billy Butler had an RBI single in the first for Kansas City, which won three of four against Tampa Bay.
Davis prevented further damage by getting an inning-ending fly from Jose Molina with the bases loaded.
The Rays announced during the game that right-hander Alex Cobb, who was hit on the right ear by a liner off the bat of Kansas City's Eric Hosmer in the fifth inning on Saturday night, had been discharged from Bayfront Medical Center.
"I know we feel wonderful about it," Maddon said. "I think the rest of baseball feels good about it."
Tests showed Cobb has a mild concussion. He was put on the 7-day concussion list, and Tampa Bay recalled right-hander Josh Lueke from Triple-A Durham.
In a message posted on his Twitter account, Cobb thanked Rays head athletic trainer Ron Porterfield and the doctors at Bayfront, and said that he, "Woke up with only a minor headache today."
There was a loud cheer from the announced crowd of 27,442 at Tropicana Field when the news about Cobb was posted on the scoreboard after the top of the sixth.
To make room on the roster for Myers, INF Ryan Roberts was optioned to Durham. ... Tampa Bay LHP David Price (strained left triceps) isn't ready to start a minor league rehab assignment. He will have another bullpen session on Tuesday. ... The Royals flew in 21 fathers and two sons of team personnel to be together for Father's Day. "I've never heard of anybody doing this before so I think it's a special treat for everybody," Yost said. ... Rays 3B Evan Longoria (right foot) was the DH for the fourth consecutive game. Maddon hopes Longoria will be able to play in the field on Tuesday. ... Kansas City LHP Danny Duffy (elbow ligament replacement surgery) made his second rehab start Saturday night for Triple-A Omaha. He gave up two runs, four hits and three walks in three innings.