The 28-year-old Hochevar has struggled to a 4-7 record and a 5.65 ERA in 14 starts this season, but he was dominant in a 2-0 victory over the Astros last Tuesday.
Hochevar carried a no-hitter into the fifth and ended up scattering five hits over 7 2/3 innings in earning his first win since May 12.
Hochevar was happy with his performance.
"It's starting to come together," he said. "The main thing is making good pitches. That's where my focus has been. That's where I plan on staying. Just going out and executing quality pitches one at a time."
Royals manager Ned Yost hopes Hochevar is beginning to find a comfort zone.
"That was a tremendous ballgame from Luke Hochevar," Yost said. "He's getting back to who he is. He was as good as he could be [against the Astros]."
The 24-year-old Cobb, who was recalled from Triple-A Durham on May 19 to take injured Jeff Niemann's place in the Rays' rotation, was sensational against the Marlins in his last start on June 17.
Cobb (3-3, 3.82) pitched seven innings and yielded zero runs and just two hits while striking out a career-high 10 in a 3-0 Rays victory.
In his sixth start of the season, Cobb was economical, throwing 100 pitches, 69 for strikes.
Tampa Bay considered bringing Cobb back for his next start on Saturday in Philadelphia, but a Friday rainout negated that and the Rays elected to send him ahead to Kansas City on Sunday afternoon before their day-night doubleheader with the Phillies.
Cobb said the uncertainty of when he pitches doesn't bother him.
"I'm not too picky when it comes to that stuff," he said. "Things happen in the game and you have to be able to make adjustments. I'm not going to complain any time I get extra rest."
Rays: Price first to 10
Left-hander David Price became the American League's first 10-game winner by beating the Phillies in the first game of of Sunday's doubleheader.
Second baseman Brooks Conrad went 2-for-3 with four RBIs in Sunday's second game, the most RBIs he's had in a game since July 24, 2010.
Royals: Hosmer still struggling
First baseman Eric Hosmer, who hit .293 with 19 home runs and 78 RBIs in 128 games after being promoted from Triple-A Omaha last season, has not been able to get it going in 2012.
Hosmer, who was given a day off Sunday against the Cardinals, is hitting .213 with eight homers and 33 RBIs. The first baseman is hitting just .158 in his last 11 games.
Yost penciled third baseman Mike Moustakas into the third spot in the batting order for Sunday's game and the left-handed slugger responded with a 3-for-5 performance that included two home runs. He has 12 homers and 36 RBIs for the season.
Rays center fielder B.J. Upton went 0-for-4 with four strikeouts in Sunday's second game against the Phillies. Upton had struck out a combined five times in his previous six games.