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Beltre, batting .516 over his past eight games, matched a career high with six RBIs and finished a double shy of the cycle after his ninth-inning triple helped put the game out of reach.
Ortiz, who batted third for the first time in a year, homered for the sixth time in his last 11 games and ninth time this month.
"We know we're good. We just have to sustain it over 162 games," second baseman Dustin Pedroia said after Boston won for the eighth time in nine games to improve to a season-best six games over .500 (27-21) after struggling much of April.
"We started out real slow and everybody kind of panicked," Pedroia added. "We have confidence we're going to win a lot of games, and hopefully the way we're playing will continue for a long time. We're still climbing. We're letting everybody know we're not going anywhere."
The Rays, who have baseball's best record at 32-15, aren't surprised.
"They've got a lot of good things going on, too," Tampa Bay manager Joe Maddon said.
"They're not going away. We're not going away. The Yankees aren't going away. Toronto's still playing well. It's a tough division."
Boston improved to a season-best six games over .500 (27-21) and has gone 23-12 since being swept by the Rays in four games at Fenway Park from April 16-19. Tampa Bay, whose three-game losing matches its season high, is 22-12 since then.
"It was nice to contribute and make sure we get the sweep against the team that's in front of us," Beltre said. "It was huge. We remember that they did the same to us at our home."
Beltre hit a solo homer off Matt Garza (5-3) in the second inning, and his three-run shot off the Tampa Bay starter made it 4-1 in the third.
Ortiz's ninth homer in May was a two-run blast that increased the lead to 6-2 in the fifth. The slugger has 23 RBIs this month after driving in just four in April.
Meanwhile, John Lackey (5-3) allowed two runs over 6 1-3 innings, pitching his best with runners in scoring position.
The Rays were 2 for 25 with in key situations in the series, including 1 for 13 against Lackey, who gave up two runs and eight hits. No. 9 hitter Reid Brignac drove in both the runs off him.
Garza, who pitched eight shutout innings during a 7-1 victory over the Red Sox at Fenway Park last month, allowed a season-high six runs and five hits in five innings - matching his shortest outing of the year.
"There are certain things we've been doing well that we did not do well the past three days," said Maddon, noting the Rays' deficiencies in situational hitting and starting pitching in two of the three games.
"They got the outs they needed," Maddon added. "We did not."
The Rays roughed up Lackey during their four-game sweep in Boston, scoring eight runs off the right-hander over 3 1-3 innings. With some timely hitting, they might have been able to get the best of him again.
Instead their offensive woes continued with Lackey repeatedly working out of jams. Brignac grounded out in the second to drive in Tampa Bay's first run, then slapped a single to left-center field to trim Boston's lead to 4-2 in the fourth.
Boston's bullpen was nearly perfect in the first two games of the series, allowing one baserunner in six innings, and did the job again.
Hideki Okajima got two outs in the seventh. Ramon Ramirez pitched a perfect eighth before Joe Nelson gave up a solo homer to Ben Zobrist in the ninth.
Beltre's two-run triple off Lance Cormier was the biggest blow in Boston's five-run ninth. Jeremy Hermida had a RBI single and Darnell McDonald added a two-run double.
This program aired on May 27, 2010. The audio for this program is not available.
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