ST. PETERSBURG, Fla. — Remember early in the year when Eric Hosmer seemed to hit one line drive after another and have little to show for it?

Here on Tuesday night was the law of averages squaring accounts — at least a little.

Hosmer floated a two-out RBI single into center field in the 10th inning that lifted the Royals to a 1-0 victory over the Tampa Bay Rays 1-0 at Tropicana Field.

“We’ll see,” Hosmer laughed. “I feel like there’s still a good amount of making up to do. But this one … didn’t hit it too hard, and I didn’t hit it too soft. Perfect spot. I’ll take it.”

So will the Royals, who won for just the fifth time in their last 27 games at the Trop.

The end came after a magnificent pitchers’ duel through eight innings between Royals right-hander Luke Hochevar and Rays lefty David Price. Relievers Kelvin Herrera and Fernando Rodney protected the twin shutouts through the ninth.

The winning run, perhaps fittingly, was unearned.

The Royals cashed a two-out chance in the 10th against Joel Peralta — remember him from the 2006-08 Royals? Jeff Francoeur reached on a single to deep short and took second when Ben Zobrist threw wildly to first.

“I did a good job of looking to the right,” Francoeur said, “like they actually teach us. I did what I was supposed to do. I saw I could get to second. We had to get a guy into scoring position. We knew we just needed one run. I think they knew the same thing.”

Hosmer then sent a soft looper into center that fell beyond Zobrist and in front of B.J. Upton for an RBI single. Francoeur scored without a throw.

“Watching Zobrist go after it,” Hosmer said, “he was running in circles out there, and I didn’t think he had a good bead on it. I was just hoping it would fall.”

Herrera, 1-1, got his first major-league victory — which led to the ritualistic post-game beer shower — when Greg Holland closed out the victory with a one-two-three inning.

“I’m smell like shampoo, baby powder and beer,” Herrera said, “but it’s great. It’s like the first day I got here in the big leagues. It’s a big day in my life.”

Holland is perfect in six save opportunities since becoming the Royals’ closer following a July 31 trade that sent Jonathan Broxton to Cincinnati for two minor-league pitchers.

Peralta, 1-5, was the loser.

Herrera worked around a mistake — by Hosmer — in the ninth inning that produced Tampa Bay’s second hit: Matt Joyce reached on a two-out single to the right side when Hosmer broke late to first base.

“That was a slow-hit ball,” Hosmer said, “and Gio (Johnny Giavotella) was playing pretty deep. I wasn’t sure if he was going to get to it. I broke to the bag late, and it was my fault because I didn’t tell Herrera, ‘I’ve got the bag.’ ”

The two arrived together, but it was Herrera who grabbed Giavotella’s throw. But Hosmer was between Herrera and the base — and Herrera’s stab at the base with his foot was too late for the out.

Turned out, it didn’t matter because Herrera ended the inning by retiring pinch-hitter Jeff Keppinger, another one-time Royal, on a routine fly to right.

Hochevar and Price, the first overall picks in the 2006 and 2007 drafts, were thoroughly dominant before settling for no-decisions. Hochevar gave up one hit while striking out 10 and walking three; Price gave up three hits while striking out eight and walking none.

“I can’t say enough for the job that Hoch did matching up with Price,” manager Ned Yost said. “You look throughout the league, and there are five or six legitimate No. 1s, and he’s one of them.”

Price’s no-decision denied him the chance to become the majors’ first pitcher to 17 victories. It also marked the second time in four starts that he went unrewarded for eight shutout innings.

“Early on, I had a lot of hard-hit balls right at people” he said. “It was great job by our defense, but Hochevar again threw the ball well against us.”

Hochevar’s best previous outing this season was a seven-hit shutout June 25 in an 8-0 victory over the Rays at Kauffman Stadium.

This was better.

“I was just trying to make good pitches,” he said, “and I was making some good pitches. Tonight was probably the best command that I’ve had all year with my fastball.”

The Royals broke a six-game skid at the Trop and clinched the season series by improving to 4-1 with only this afternoon’s game remaining. They also won for the 14th time in 21 games.

Tampa Bay lost for the first time in six games and for only the third time in 15 games.

“Tonight from David Price, that’s the best guy we’ve faced this year” Francoeur said. “He threw every pitch where he wanted. We knew with the way Price had been pitching the last seven weeks, we had to have Hoch throw a game like he did. And he did.”

Hochevar faced trouble only in the third inning, which began with a double by Luke Scott, who went to third on Ryan Roberts’ deep fly to center. Hochevar stranded Scott by striking out José Molina and Desmond Jennings.

“I know it sounds like a broken record,” Hochevar said, “but when you get a guy on third like that in a tight ballgame, that’s really when you’ve got to buckle down and make quality pitches.”

Hochevar issued a one-out walk to Joyce in the fourth, but Salvy Perez picked off Joyce with Evan Longoria at the plate. It was Perez’s second catcher pick-off of the season. No other American League catcher entered the night with more than one.

In the end, it was all prelude to Hosmer’s game-winning single.

“We came in hot, and they came in hot,” Yost said. “They outplayed us (Monday) night, and we found a way to win tonight. That’s a good team over there. It’s a big win for us.”