ST. PETERSBURG, Fla. — Jarren Duran had a clear message for the teammates waiting for him in the clubhouse Wednesday night as he ran through the tunnel from the playing field.

“Sweep, sweep, sweep, sweep, sweep, sweep, sweep!” Duran bellowed.

After a convincing 8-5 victory against the Rays to finish a three-game sweep at Tropicana Field, the significance of winning three straight at Tampa Bay was not lost on the Red Sox.

The last time Boston swept a series there, the games included Michael Chavis’ major league debut, and solid starts from Rick Porcello and David Price. Ryan Brasier secured saves in all three games. Brayan Bello, who started Wednesday’s finale, was a 19-year-old who went on to post a 5.43 ERA in 25 games at Class A.

The Red Sox haven’t played as well at the Trop as they did this week in a while. They entered the series having lost 15 of 16 games – and 22 of 27 – at the venue. Tampa Bay had won two-thirds of the matchups between the teams in the last six seasons, going 56-28.

“It feels very good to be able to sweep the series and win here,” said Bello, through interpreter Carlos Villoria Benítez. “Obviously last year was a very bad year for us against them, and they went to our place and won three games. For us to come here and win was very important.”

The Red Sox outscored the Rays 18-7 in the series, getting strong starts from Tanner Houck, Cooper Criswell and Bello. They trailed 2-0 on Tuesday and 3-0 on Wednesday, then won both games, their first two victories after trailing by multiple runs.

Down 3-0 in the fifth inning of the finale after Tampa Bay tagged Bello for three runs in the second, the Red Sox used a patient, humble approach to bat around and score five runs.

Five players singled and seven reached base. Ceddanne Rafaela (RBI single), Connor Wong (two-run single), Rob Refsnyder (RBI single) and Dominic Smith (RBI single) were instrumental in the rally.

The Red Sox were 6 for 12 with runners in scoring position, continuing an encouraging turnaround that dates to the beginning of the current four-game winning streak that started Sunday in St. Louis.

“In this business, everybody wants to hit the ball out of the ballpark. In certain moments you’ve got to put the ball in play and we did,” said Manager Alex Cora.

“The value of putting the ball in play was huge (Wednesday) and we’re going to keep preaching that. I know some people probably hate that, but I’m the manager and I’m asking that from my players.”

Refsnyder’s 76.8 mph opposite-field bloop that put the Sox up for good was an example of exactly what the club was looking to do against relievers Richard Lovelady and Kevin Kelly.

“You never know if it’s going to come against the Rays. They have such a dominant bullpen and they have for a long time,” Refsnyder said.

“Just trying to piece together some good at-bats and the young guys did a great job. It’s nice coming back against a really, really good team.”

The Red Sox hit just five homers over the three games of the series but used an athletic, fast approach to beat the Rays at their own game.

That was especially evident Tuesday when they stole four bases (including home) in a dramatic eighth inning, and again Wednesday in the fifth.

“They changed the rules for this type of baseball,” Cora said. “It’s not that we’re going to run crazy out there but you need athletic guys to win it and to be competitive at this level. Why? Because not all the time you’re going to hit. You’re not going to hit the ball out of the ballpark all the time. But you can do the other stuff. You can play defense every day. And speed is not going to slump.”

The win also represented a bit of revenge for Bello, who entered his outing with a 6.92 ERA in five career starts (26 innings) against the Rays. He didn’t have his command early and allowed the first four hitters of the second to reach (and three to score). But he settled in with improved feel of his change-up and allowed just three baserunners in his final four innings.

Bello walked four but still was credited a quality start, allowing three runs in six innings.

“Since I was called up, (Tampa Bay) has given me a little bit of trouble,” Bello said. “But luckily in the last two, I’ve been able to pitch well against them.”

Three straight wins against the Rays represented progress toward one of Cora’s goals this season.

In addition to wanting his club to play better at home — where they’re 10-13 entering a stretch where they’ll play 15 of 22 games at Fenway — the manager wanted Boston to show improvement against divisional opponents after going a combined 50-78 (.391) over the last two seasons.

This season they’re 4-6, but chances will loom soon. The Sox will face the Orioles for three games at Camden Yards next week and will play nine divisional games in June.

Wednesday’s win finished a 4-2 road trip following a home series in which the Sox lost 3 of 4 to the Rays.

“We played well against them last week. We just didn’t win the games,” Cora said. “Two extra-inning games. We did a lot of good things throughout the road trip, but we put the ball in play. It started in St. Louis.”

The Red Sox won’t return to Tropicana Field until Sept. 17, when they begin their next-to-last road series of the season. They can only hope to play as well as they did this week.

“The Rays have been such a good team for such a long time, so it’s nice to win some games here,” Refsnyder said. “It was a really good series.”