ST. PETERSBURG -- In the middle of the fifth inning Thursday afternoon, the Rays found themselves in an unfamiliar position. They were losing.

Trailing the Red Sox by two runs on a day they’d already lost starting pitcher Jeffrey Springs to a nerve injury, the Rays didn’t panic. There was no cause for concern in their dugout, not when their relentless lineup has been finding ways to win since Opening Day.

Eleven hitters and seven runs later, Tampa Bay was well on its way to a 13th consecutive victory. The Rays’ fifth-inning rally helped them surge past the Red Sox and into the history books with a 9-3 victory before a crowd of 21,175 at Tropicana Field.

• Rays' streak has produced these incredible stats

The Rays have matched the 1982 Braves and ‘87 Brewers for the longest winning streak to start a season in MLB’s Modern Era. The only team to win more games in a row at the outset of a season was the 1884 St. Louis Maroons, who went 20-0 before losing a game.

Additionally, these Rays now own the longest overall winning streak in franchise history, as Thursday’s victory to complete a four-game sweep of Boston broke a tie with the 2004 Devil Rays (12 straight).

“Pretty amazing,” Rays manager Kevin Cash said. “No doubt when you do something like that, you’re playing really well. And there’s not one part of our game right now that we don’t feel good about.”

The Rays aren’t just winning games, either. They’ve cruised past nearly everyone they’ve faced. They’ve outscored their opponents by 71 runs (101-30), the third-largest run differential in Major League history through the first 13 games of the season and the largest in the Modern Era.

Eleven of their 13 wins have come by at least four runs. They have trailed after only six of the 117 innings they’ve played, including Thursday’s fourth inning, tied with the 1884 New York Gothams (again behind the 1884 Maroons) for the second-lowest total in MLB history.

“To go on a run like this, everything's got to be clicking, and you’ve got to get contributions from all parts of your roster,” Cash said.

That’s certainly been the case for the Rays’ lineup, which leads the Majors in runs (101), homers (32) and OPS (.940) by considerable margins. But their big inning in lucky No. 13 came without a homer, instead starting slowly before escalating quickly.

Harold Ramírez led off the fifth with a double down the left-field line against Corey Kluber, who threw the final pitch of the most recent meaningful game lost by Tampa Bay: Game 2 of the American League Wild Card Series in Cleveland last October.

After a Taylor Walls groundout, Josh Lowe worked a walk, and Francisco Mejía slapped a changeup inches off the ground to right field for an RBI single. Yandy Díaz lofted a fly ball to right field that moved Lowe into scoring position, then Brandon Lowe and Randy Arozarena followed with a pair of RBI singles off lefty reliever Richard Bleier to put Tampa Bay on top.

“We've come up with some timely hitting. That might have been the most timely to date,” Cash said. “But we got momentum, and it seemed like it was just going to continue to roll.”

It did. After Wander Franco was hit in the elbow by a pitch, pinch-hitter Manuel Margot dropped a perfectly placed bunt single to drive in another run. Then Ramírez cleared the bases with a double, capping the rally just as he started it.

“It's kind of a testament to our hitters right there to know that we don't have to stress. We don’t have to freak out,” Brandon Lowe said. “Once you get one little spark to this lineup, there's no turning back.”

Lowe tacked on a solo homer in the seventh, his fifth of the season, while reliever Braden Bristo -- a 28-year-old rookie added to the roster Thursday morning -- struck out four over three hitless innings in his Major League debut.

The Rays secured the ball from the last out of their historic victory and kept it for Bristo, commemorating his first big league save.

“If you're going to be up here, other than the playoffs or World Series, this is the kind of day you want to be up here,” Bristo said, smiling. “This is a great team in this clubhouse, and I'm just glad to play a little, small part of it on a big day.”

After celebrating Thursday’s win, the Rays weren’t yet ready to think about what comes next. They put on their tightest turtlenecks and beanies and bared their biceps as part of a dress-up trip inspired by Díaz’s singular wardrobe, then left the ballpark and boarded a flight bound for Toronto.

They’ve come this far. Why stop at 13-0?

“Nobody likes to tie,” Brandon Lowe said with a grin.