ST. PETERSBURG -- At 1:35 a.m. ET on Tuesday, Rays pitching coach Kyle Snyder missed a call from Drew Rasmussen. About 20 minutes later, Rasmussen’s late-night call to manager Kevin Cash also went unanswered.

Rasmussen was trying to get a hold of both to let them know he was headed to the hospital with his wife, Stevie. She delivered their first child, a healthy baby boy named Rhett, three days earlier than expected and about 14 hours before Rasmussen had been expected to start for the Rays against the Red Sox.

Snyder and Cash sent their well-wishes to the Rasmussens on Tuesday morning, then they almost immediately went to work formulating a pitching plan that worked out just fine. With Rasmussen on paternity leave and plenty of early run support, an opener and five relievers limited the Red Sox to six hits and delivered the Rays an 8-4 win at Tropicana Field.

“It was a little bit of a mad dash today. The guys knew that it was going to be kind of a creative bullpen day,” Cash said. “Just appreciate the workload of everybody that we were able to get through the ballgame.”

Their effort led the Rays to their 18th win in 23 games since Aug. 13, a stretch in which they have outscored their opponents by 63 runs (122-59), pushed them to a season-high 18 games over .500 (76-58) and reduced their deficit in the American League East to 4 1/2 games.

A bullpen game isn’t necessarily anything out of the ordinary for the Rays, who are accustomed to using openers and leaning heavily on a relief corps that’s pitched more innings than any other group in the Majors. But these circumstances were unusual, because Tuesday’s game became a bullpen affair in the middle of the night.

“Between [president of baseball operations Erik Neander] and I and Kyle, we were talking pretty early in the morning,” Cash said. “But [we] had a good sense that we were in good enough shape to be able to kind of piece it together.”

So rather than sending the AL Pitcher of the Month to the mound, the Rays sent JT Chargois for two innings as an opener, and then used Garrett Cleavinger, Calvin Faucher, Brooks Raley, Jalen Beeks and Jason Adam to get through the rest of the game.

Boston’s lineup did all its damage with a pair of two-run homers: Triston Casas’ first career homer off Chargois in the second inning and Tommy Pham’s shot off Beeks in the eighth. But the Rays’ relievers otherwise held the Red Sox to four singles and two walks while striking out 10.

Cleavinger struck out three over his two innings and was awarded the win, his first with Tampa Bay. That made him the 24th Rays pitcher with a win, the most in the Majors this season and tied with the franchise record set in 2018.

“I think the bullpen stepped up to do what we do,” said Raley, who lowered his ERA to 2.12 as he struck out two over two innings. “Obviously, Boston's a very good team, and the runs early really helped kind of get guys settled in.”

After being shut out for seven innings by Red Sox starter Rich Hill on Aug. 27 at Fenway Park, the Rays didn’t let him settle in on Tuesday night. Yandy Díaz hit a leadoff double, Manuel Margot singled and Randy Arozarena launched his 19th home run of the season to center field, smashing a WiFi antenna in the process with his three-run blast.

“When we score early, it gives us confidence throughout the rest of the game to play a little bit more relaxed,” Arozarena said through interpreter Manny Navarro, “and it gives the pitching staff a little bit more of an ease when they pitch the game.”

Harold Ramírez helped them relax even more in the third. On his 28th birthday, Ramírez knocked a two-run single to left field that restored the Rays’ three-run advantage. Christian Bethancourt and Yu Chang hit back-to-back homers off reliever Eduard Bazardo in the sixth, and Francisco Mejía doubled in another run in the seventh.

The Rays are averaging five runs per game since Aug. 4, and 5.92 per game over the past two weeks. Tuesday’s outburst -- their 13th three-homer game this season, but only their second since the All-Star break -- was further proof they can score -- and win -- in a variety of ways.

“We’re getting better and better every day,” Ramírez said.