Beltre matched a career high with six RBIs and finished a double shy of the cycle after his ninth-inning triple 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.
John Lackey (5-3) allowed two runs over 6 1/3 innings, pitching his best with runners in scoring position. The victory was the eighth in nine games for the Red Sox.
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.
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, which has the top record in baseball at 32-15, is 22-12 since then.
The Rays were 2-for-25 with runners in scoring position 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 on April 18, allowed a season-high six runs and five hits in five innings — matching his shortest outing of the year.
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 blow in Boston's five-run ninth. Jeremy Hermida had a RBI single and Darnell McDonald added a two-run double.
Notes
Slumping Rays CF B.J. Upton, batting .146 in his last 23 games, had the night off. … Red Sox CF Jacoby Ellsbury was out of the lineup for the second straight night because of soreness in his left side. RF J.D. Drew, who's been bothered by a sore hip flexor, was also out of the lineup, as was C Victor Martinez, who left Monday's series opener after being hit on the left big toe by a foul ball. … Crawford stole second base in the fourth inning, giving him 32 straight successful steals against the Red Sox, who have not thrown him out since on Sept. 21, 2005.