For about an inning and a half on Thursday the Tampa Bay Rays trailed by a couple of runs and actually appeared in danger of losing, or at least the concept seemed plausible.

It was a mirage.

Over their first 13 games, the rollicking Rays have been invincible, plowing past old benchmarks for early-season success and forcing historians to search back across three centuries to find anyone who did it better.

The Rays beat the Boston Red Sox, 9-3, Thursday in St. Petersburg, Fla., to extend their record to 13-0, yanking the attention of the baseball world away from rule changes and pace of play and refocusing it on one of the best starts to a season since players wore pillbox hats and cardigan sweaters.

Tampa Bay tied the modern era record, which dates to 1900, for consecutive wins to open a season, joining the 1982 Atlanta Braves and the 1987 Milwaukee Brewers. They open a weekend series against the Blue Jays in Toronto, and if the Rays win on Friday, they will stand apart from any big-league team currently in existence.

“When you do something like that, you’re playing really well,” Rays Manager Kevin Cash told reporters after the game. “There is not one part of our game right now that we don’t feel good about.”

The 13 victories also set a franchise record for consecutive wins at any point in a season, surpassing a 12-game heater in June 2004 under Lou Piniella.

Coincidentally, Thursday’s game was also the Rays’ 13th consecutive win over Boston at Tropicana Field, a period of domination dating to last April.

Only one club has gone undefeated longer to start a season, and that happened less than 20 years after the Civil War. The 1884 St. Louis Maroons, a team in the Union Association that included star outfielders like Buttercup Dickerson and Orator Shafer, opened at 20-0. St. Louis finished the U.A.’s only season with a 94-19-1 record, 25 more wins than the closest team.

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

That is a Tampa Bay specialty. The data-reliant Rays, who have made the postseason in each of the last four seasons and won the American League pennant in 2020, have long been characterized as consistently successful despite their low player payrolls and their outdated domed stadium with modest attendances and revenues.

In the highly competitive A.L. East, with perennial powerhouses like the Yankees, the Red Sox and the Blue Jays, the Rays have uncovered and developed excellent players and have turned that into winning results. But nothing like this current run. This team’s opening day payroll was $73.1 million, according to Cot’s Baseball Contracts, 28th in the 30-team league.

Granted, their early schedule has not been taxing. They have faced Detroit, Washington, Oakland and Boston, four teams with low expectations. But Tampa Bay is not the first team in the 123 seasons of the so-called modern era to ease into the season with a relatively soft opening slate, and only three teams have ever started 13-0.

Going back to the 19th century, the 1884 Maroons, who went on to briefly join the National League after the Union Association shut down, outscored their opponents by an average of 4.02 runs per game, according to Baseball Reference. The Rays, with a run differential of +71, are winning their games, on average, by 5.5 runs.

They have had only a single one-run game this year, and before Wednesday they had won 10 of their first 11 by at least four runs. One of the most telling statistics to illustrate their dominance is that in their 10 home games, they have never batted in the bottom of the ninth inning.

The list of crazy achievements is extensive. They took down Oakland by 11-0 on Saturday. For those who missed it, Tampa Bay provided an encore the next day. Two 11-0 wins in a row over the same team.

The Rays have hit more home runs (32) than they have given up runs (30). Just two weeks into the season, they have 10 players with at least two home runs and seven with at least three.

Not surprisingly, the Rays led the majors after Thursday’s game in runs scored (101), total bases (249) and on-base plus slugging percentage (.940). Also not surprising, their pitchers led baseball in E.R.A. (2.23) and had the lowest batting average against (.189).

“As far as the pitching goes, the overall execution has been pretty remarkable,” Cash said after Wednesday’s win over Boston.

The pitching success has been achieved without the help of Tyler Glasnow, who has been out with an oblique strain. Zach Eflin, another top starter, who signed with the team as a free agent in the off-season, won his first two starts but was placed on the injured list with lower back tightness. Then on Thursday, Jeffrey Springs, the left-handed starter, exited the game with ulnar neuritis in his left elbow. His status was unclear.

But in the short term, it was no problem. Kevin Kelly came out of the bullpen and earned his first big league win and Braden Bristo made his major league debut, earning the save with three hitless and scoreless innings.

No matter who has entered these games, they mostly perform well. That was the case Wednesday when Taj Bradley, a top pitching prospect, made his major league debut on his mother’s birthday.

Ana Mosley watched and cheered from the stands as Bradley threw five strong innings for the win, allowing three runs, five hits and a walk and striking out eight. Bradley, a right-hander, was notified on Tuesday of the call-up from the Class AAA Durham Bulls and had one hour to pack and get to the airport for a flight to Tampa, Fla., amid a rush of activity and phone calls.

He pitched through the first inning like a 10-year veteran, but when he returned to the dugout, the long-awaited moment briefly overwhelmed him.

“After the first inning I got pretty emotional,” he said in an interview with WDAE, the Rays’ radio broadcaster. “I had to cover my face with a towel. I had some tears going. After getting out of that first inning, I was excited, man. It’s a dream come true, a childhood dream come true.”

Randy Arozarena, the Rays’ slugging left fielder, hit his third home run of the season on Wednesday, and shortstop Wander Franco was 3 for 5 with two R.B.I. and two runs scored, increasing his batting average to .340. Franco has four home runs.

“Wander’s on fire right now,” Cash said.

The entire team is hot. On Thursday, Yandy Díaz, the first baseman, hit his fourth home run and second baseman Brandon Lowe hit his fifth in five straight starts — talk about streaks.

Of course, a season-opening winning streak does not guarantee success. The 1982 Braves lost to the eventual World Series champions, the St. Louis Cardinals, three games to none, in the N.L. Championship Series, and the 1987 Brewers won 91 games, but finished third in the A.L. East and missed the postseason. That Milwaukee team, after winning 13 in a row in April, lost 12 in a row in May.

No one expects that kind of evening up for the Rays, but at some point, they will lose. Not even the 1884 St. Louis Maroons were truly invincible.