Manny Ramirez also homered twice and had three RBI for the Red Sox, who still lead the New York Yankees by a half-game after the Yanks edged the Baltimore Orioles 12-9.
Ortiz now leads the AL with 46 home runs as the Red Sox try to fend off the charging Yankees. The teams meet in a three-game series to end the regular season September 30-October 2.
Boston smacked 21 hits against the Devil Rays and tied an AL record with four players (Trot Nixon, Jason Varitek, Ortiz and Ramirez) getting four hits apiece.
"They have their backs against the wall right now," Tampa Bay second baseman Julio Lugo said of the Red Sox. "Tonight they made a statement."
Nixon, Ramirez and Ortiz each scored four times for Boston, while Nixon drove in three runs.
Ortiz continued his torrid hitting, which drew appreciation from Boston manager Terry Francona.
"(John) Olerud had the best line, 'They need to put out a public address and tell the children to be careful."' Francona said.
Curt Schilling (7-8) pitched seven effective innings, allowing two runs on six hits with seven strikeouts, before leaving with a 13-run lead.
Boston had three runs in the first, four in the third, three in the fourth and three more in the fifth en route to the easy win.
Seth McClung (6-11) allowed seven runs on seven hits in two innings and took the loss. Three relievers didn't fare much better against Boston's relentless offence.
"I couldn't believe they kept hitting those balls out," McClung said.
Jorge Cantu hit a solo home run in the first and had a sacrifice fly in the third to account for the Tampa Bay runs.
SHEFFIELD STARS
In New York, Gary Sheffield belted a grand slam and drove in six runs as the Yankees beat the Baltimore Orioles 12-9, keeping pace with the Red Sox.