Kansas City's lineup -- missing Alex Gordon and Mike Aviles -- caught a lift from Esteban German's two-out, two-run single and applied some early pressure to Rays starter James Shields, who has been particularly dominant at home.
But with two outs in the third inning, the Rays exposed some cracks in Hochevar's early composure.
The Rays capitalized on the young right-hander's predictability, notching three straight hits -- including a two-run homer by Evan Longoria -- to put Hochevar on the ropes.
"Very good in the first, a little shaky in the second, the wheels feel off in the third," manager Trey Hillman said of Hochevar. "Just consistency in making pitches."
Hochevar was almost too consistent in pitch selection on Sunday, as he admitted that he too often lived down and on the inside corner.
"Just me not making adjustments," he said of the big inning. "First pitch, they are coming out of their shoes. That tells you they are looking for pitches, and they are looking for location. I just got to do a good job of changing that, moving the ball around."
While Shields got into a groove following a second-inning hiccup, Hochevar's woes spilled over onto the field.
The young hurler was late covering first base on a double-play attempt and let Willy Aybar take third base freely in the third inning.
"Those are plays that you have to make, and mistakes that you can't," Hochevar said. "I just got caught in between on that ball to first. But there's no excuse for that; I've got to get over and cover the bag."
Hillman agreed, and said that Hochevar's struggles let the Royals' early momentum disappear.
"You can't do that to a hot team," Hillman said. "[The Rays] are hot. They are confident. Can't make that many mistakes."
By the time the Rays tacked on a pair of two-out runs in the fourth inning, the five-run Royals deficit felt much larger, as Kansas City was held to three hits and no runs over the final seven frames.
"When you are playing a team that is this good, they are confident they can come back," said Jose Guillen, who was one of five players named to the American League Final Vote ballot on Sunday.
"They've been pitching great, really confident, so you have to give some credit to them over there."
The Royals have been outscored 23-4 in first three games of this series, averaging five hits per game.
"They are doing everything they need to do," added Guillen, a former member of the Rays. "It is a total team effort over there. It is good to see."
The rolling Rays have now won seven straight games, and the Royals will need to make adjustments on the mound and at the plate if they hope to avoid a four-game sweep tomorrow.
As the Rays' newfound confidence continues to add steam, the Royals find themselves in a three-game skid for the first time since June 3-5. Coming off a 16-11 record in June, Kansas City has dropped five of its first six games since the calendar flip.
A win on Monday would lessen the sting before Kansas City embarks on the final week before the All-Star break.
"Hopefully we can [win]," Hillman said. "We can't do it without quality pitching."