ST. PETERSBURG, Fla. (AP) — Worst to first — and now the World Series.

Take that, nonbelievers. These Tampa Bay Rays have arrived.

They proved it Sunday night, dethroning the defending champion Boston Red Sox with a 3-1 victory in Game 7 of the AL championship series.

Down to their last chance after nearly letting it all slip away, the Rays completed a stunning run to their first pennant.

‘‘I used to tell people I played for the Devil Rays and they’d ask, ’Who are the Devil Rays?’’’ said center fielder B.J. Upton, who had four homers and 11 RBIs in the ALCS. ‘‘Now, I think they know who we are.’’

A 200-1 shot to win the title before the season, the Rays will host the Philadelphia Phillies in Game 1 Wednesday night. Manager Joe Maddon’s bunch is trying to become the first team to go from worst in the majors to World Series champion in just one season.

‘‘I hope everyone doubts us again,’’ reliever J.P. Howell said. ‘‘Philly’s a better team than us. That’s all I’ve got to say.’’

Right-hander Matt Garza beat Boston lefty Jon Lester for the second time in a week to earn MVP honors.

Meanwhile, rookie David Price put an exclamation point on why Tampa Bay’s future looks so bright by getting the final four outs to begin the celebration.

‘‘There’s nothing else to say other than I would’ve never thought this in a million years,’’ said designated hitter Cliff Floyd, one of the veterans brought in last winter to provide leadership and stability in a young clubhouse.

‘‘It’s amazing what can happen when you put a lot of athletes on the field and start to believe during the course of the season. It was only a matter of time before it became this.’’

To finish the task, the Rays even showed a bit of Boston-like resolve when they needed it.

After squandering a seven-run lead late in Game 5 and losing meekly Saturday night, few gave Tampa Bay a chance in Game 7 against Lester and an experienced Red Sox team seeking its third berth in the World Series in five years.

But when Price struck out J.D. Drew with the bases loaded to end the eighth inning, the Rays were on their way.

Price, who didn’t make his major league debut until late September, also worked the ninth, walking Jason Bay and striking out Mark Kotsay and Jason Varitek before getting pinch-hitter Jed Lowrie to ground into a game-ending force play.

‘‘He was the cherry on top of the icing on top of the cake,’’ Rays principal owner Stuart Sternberg said.

When it was over, players and coaches streamed from the dugout and mobbed Price, eventually falling to the ground in a cluster that continued to grow when others began leaping on the pile.

Music blared and the crowd of 40,473 stood and cheered.

The party moved inside briefly before players returned to the field raced up and down the right-field stands spraying fans with champagne before settling down for the presentation of AL championship trophy.

‘‘It’s not what we expected to happen,’’ Boston slugger David Ortiz said. ‘‘You have to give them credit. They pitched well. They’ve got good hitters.’’

Willy Aybar homered and Evan Longoria and Rocco Baldelli also drove in runs to support Garza. Acquired in an offseason trade with Minnesota, Garza limited the Red Sox to Dustin Pedroia’s first-inning home run and Bay’s seventh-inning single before turning the game over to the bullpen.

‘‘This is beautiful. This is the perfect story,’’ first baseman Carlos Pena said. ‘‘It was difficult, but it makes it so much sweeter.’’

Longoria’s fourth-inning double off Lester tied it at 1-all. Baldelli’s RBI single put the Rays ahead in the fifth after Aybar doubled and Dioner Navarro reached on an infield single.

Garza took the mound for the biggest game of his life with something, perhaps cotton balls, stuffed in his ears to help drown out the noise at sold-out Tropicana Field.

The 24-year-old right-hander struck out nine before shortstop Jason Bartlett booted Alex Cora’s ground ball for an error, leading off a tense eighth.

Boston went on to load the bases when Kevin Youkilis drew a two-out walk. Price, the No. 1 pick in the 2007 draft, became the fifth Tampa Bay pitcher of the inning — quite a spot for someone who started the year in Class A.

Drew, who capped the Game 5 rally with a ninth-inning single, struck out with a check-swing on a 97 mph fastball to end the threat. Price worked around a leadoff walk in the ninth and when Lowrie grounded out, the celebration began.

‘‘I wanted the ball,’’ Price said. ‘‘Everybody down there in the ’pen wanted the ball tonight.’’

The Rays dropped the ‘‘Devil’’ from their name before the season and came out with a new identity: Gone were the laughable losers who finished last in the AL East in nine of their first 10 seasons, the snowbird specials whose quirky Tropicana Field filled with transplanted Bostonians whenever the Red Sox visited.

After splitting the first two games of the series at home, though, it was Tampa Bay that made itself at home in an opponent’s ballpark, with the Rays sending shot after shot sailing over the Green Monster. In all, the Rays outscored the Red Sox 29-13 in the three games at Fenway Park, hitting 10 home runs.

But the young Rays’ postseason inexperience showed in Game 5, when a normally reliable bullpen blew a 7-0 lead over the last three innings, allowing Boston to save its season with an 8-7 victory.

The Red Sox were the eighth team to rally from a 3-1 deficit to force Game 7 of a league championship series, and they’re the only club to do it more than once. The Red Sox also battled back in 1986, 2004 and 2007, and went on to win the World Series the last two times.

‘‘We didn’t get as far as we wanted. We got beat by a very good team,’’ Boston manager Terry Francona said. ‘‘They’ll represent the American League very, very well.’’

No team has repeated as World Series champion since the New York Yankees won three straight from 1998-2000. … Boston was 9-0 in ALCS elimination games under Francona before Sunday night. … Longoria drove in eight runs in the ALCS, the most by a rookie in a postseason series since Pat Duncan had eight RBIs for Cincinnati in 1919.