"Of course, man. These guys have been giving us a hard time," Ortiz said after he and Kevin Youkilis homered in support of right-hander Clay Buchholz in a 6-1 victory Monday night.
"Not only to us, to everyone," the slugger added. "They have the best record in baseball. So you've got to play your best."
The Red Sox beat the Rays for the first time in five tries, climbing a season-best four games over .500 (25-21) with their third straight win on a difficult road trip that began in Philadelphia.
Buchholz (6-3) won his eighth consecutive road start dating to last August, the longest such streak by a Red Sox pitcher since Roger Clemens won nine in a row from July 18, 1992 to April 20, 1993.
The right-hander allowed one run - Carlos Pena's eighth homer - and six hits over six innings. Hideki Okajima and Daniel Bard didn't allow any baserunners the rest of the way.
"We're getting great starting pitching. When you do that, all we have to do is put a couple runs on the board and those guys can take over," Dustin Pedroia said, adding the Red Sox are focused on themselves - not catching the first-place Rays.
"We're in the middle of the year and just playing," Pedroia said. "We're playing some really good teams and just finding ways to win. That's a real good sign."
Ortiz homered for the fifth time in his last nine games, hitting a solo shot off Wade Davis (4-4) in the second inning. Davis walked in a run and yielded RBI singles to Adrian Beltre and Jeremy Hermida during a three-run third that put the Red Sox up 4-0.
Youkilis, who is batting .400 (12 for 30) with five homers and 12 RBIs over his last nine games, made it 6-0 with a two-run shot off reliever Lance Cormier in the fourth.
Pedroia had three hits after beginning the night in an 0-for-19 slide. Beltre also finished with three hits for the Red Sox, who began their six-game trip by winning two of three against the NL champion Phillies.
"They got us tonight," Rays manager Joe Maddon said. "We didn't play badly. They beat us."
At 32-13, the Rays are off to the best start in the major leagues since 2001, in part because of a 19-5 road record that includes a four-game sweep of the Red Sox at Fenway Park in April. The six-game lead they carried into Monday was the largest they've ever held in the AL East.
Buchholz, who's won five of his last six starts, walked one and struck out eight. But it wasn't an easy outing.
The Red Sox starter escaped a bases-loaded jam when John Jaso grounded into an inning-ending double play in the first inning. He wiggled out of another tight situation by striking out Reid Brignac and Jason Bartlett to strand two more runners in scoring position in the second.
"We had our opportunities early," Maddon said, "and we didn't take advantage."
Pena homered with two outs in the fourth.
Boston's Victor Martinez left in the third inning. Bartlett fouled a pitch off the catcher's left big toe in the second, and Martinez had trouble walking - much less running - after drawing a walk in the third.
X-rays were negative.
"He's day to day, like we all are," Red Sox manager Terry Francona said. "But I think it's to the point where I don't think we have to make a roster move."
This program aired on May 25, 2010. The audio for this program is not available.