BOSTON — Before the game, David Price goofed around in the clubhouse with Koji Uehara’s 9-year-old son, Kaz, teaching him variations of hand slaps and handshakes.

The affable Price, 30, is truly a kid at heart.

During Sunday’s game, you might say he manned up, pitching eight scoreless innings in a 4-0 win over the Tampa Bay Rays. In 19 starts with the Red Sox, it was the first time Price held an opponent scoreless. And he also broke a 10-game streak of allowing at least one home run.

“Today is an example of what everyone sees of David’s capabilities,” Red Sox Manager John Farrell said.

Farrell and team president Dave Dombrowski have been adamant about improving the last two spots in the rotation. But everyone knows the Red Sox need better output from their No. 1.

Price is 9-6. He has pitched 1241/3 innings, including five eight-inning games in his last seven starts.

But that hasn’t been enough.

“He’s doing exactly, from an innings standpoint, what we hoped,” Farrell said.

But the Red Sox also hoped for an ERA better than 4.34, which is an improvement from his 4.74 ERA at the end of June.

The critics may point out that Price shined Sunday against the dead-in-the-water Rays, the worst-hitting team in the American League and losers of 21 of their last 24 games.

One of those three Tampa Bay wins, however, was against Price on June 29, when he gave up four runs in 61/3 innings. Price’s other start against his old team was a 32/3-inning effort in which he allowed eight runs on April 21.

So beating the Rays was not a given. Price figured it out.

“I have a good memory. I know how they’ve hurt me and what I need to do,” Price said.

After previous starts, Price emphasized “I need to get better.” He was more upbeat Sunday.

“I was never discouraged. I never lost confidence in my abilities,” he said. “I haven’t pitched as deep into ballgames, here and there, as I should. Just continue working.”

Just as Price says he turns the page after a bad performance, he seemed to be already moving on after a good one.

“What I did today is not going to matter when I pitch next,” Price said.

Price will pitch Sunday in Yankee Stadium. The pesky New Yorkers are hanging around with a 44-44 record. They will want to come out of the All-Star break on fire.

Price will need to do what he did against the Rays, locating 95 mph fastballs low and on the corners, while mixing in change-ups and cut fastballs.

The amazing part of Price’s performance was he began with a 27-pitch first inning, giving up a two-out double and a hit batsman. He needed only 86 pitches over the next seven innings, and did not allow a hit after the third inning.

“More efficient as the game went along,” Farrell said. “He was driving a lot of pitches through the strike zone, especially the bottom of the zone. He stayed out of the middle of the plate.

“Very powerful eight innings of work today … I don’t want to say he cruised, but he was in complete control of this one.”

Stephen Wright (10-5, 2.68, 114 innings in 17 starts) and Rick Porcello (11-2, 3.66, 113 innings in 18 starts) have been pitching well. If Price establishes himself as the ace he is supposed to be, Boston will take a big step toward being a World Series contender.

“When you (have) the three guys at the top of the rotation with some stability and consistency, that sure goes a long way,” Farrell said. “It takes some of the load off that bullpen.”

The bullpen may need to work overtime when someone else starts. Farrell said Eduardo Rodriguez (1-3, 8.59, 291/3 innings in six starts) is rejoining the rotation, and he plans to work Clay Buchholz (2-8, 6.31, 711/3 innings in 13 starts) back in as a starter.

Should they both continue to fail, Dombrowski will have to find a solution.

As for the No. 1 pitcher, Boston can do nothing but hope Price gets better.

Sunday was a positive sign.