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“They didn’t make any mistakes. You could see their grit,” Maddon said. “They’ve got a bunch of gamers over there. … On the other side, I think our guys were equally as tough. We have had a hard time hitting their pitching staff.”

Making their fourth playoff appearance in six years despite having one of the lowest payrolls in baseball, the budget-minded Rays have not advanced past the division series since reaching the 2008 World Series.

Xander Bogaerts scored the tying run on Joel Peralta’s wild pitch in the seventh and Victorino followed with an RBI infield single. Pedroia drove in Bogaerts with a sacrifice fly in the ninth to make it 3-1, and Uehara struck out Evan Longoria to end it.

“It feels outstanding. This is what you play for,” said Peavy, who allowed one run and five hits in 5 2-3 innings. “That Tampa Bay team is outstanding. Hats off to them. They are an outstanding baseball team — well-coached and they played hard. We knew each other very well, so it’s tough. I can’t tell you how happy I am and the rest of these guys.”

When it was over, the Red Sox mobbed Uehara in front of the mound, then took the party inside to the clubhouse, where music blared and champagne flowed.

The Rays retreated to a solemn clubhouse.

“Obviously, everybody is disappointed right now. Joe (Maddon) came in here and said to not hang our heads and remember that we had our backs against the wall several times and played really well to get to this point,” second baseman Ben Zobrist said. “It was a good year overall, but it’s tough to take the loss.”