Red Sox ace Jon Lester made his first start of the spring, firing three innings of one-hit ball. The lefty walked one and struck out four.
"I felt good," said Lester. "It felt good to get the first one out of the way. Kind of what we talked about last week as far as getting used to the surroundings and the fans and the whole routine of a normal work day. It was good. It was a step in the right direction going through spring."
Odorizzi gave up two hits and a run over 2 1/3 innings.
Lefty Erik Bedard, who is also in the mix for the Rays' final rotation spot, served up a mammoth blast to Napoli over the Green Monster in left-center in the sixth.
Rays third baseman Evan Longoria drilled a solo homer over the Monster and out of the park in the fourth against lefty Chris Capuano, who went three innings and allowed one run.
Will Middlebrooks added an RBI double and an RBI single for the Red Sox. Shane Victorino was hit by a pitch and scored a run while playing three innings in right field in his first game this spring.
Grady Sizemore, who continues to impress in his comeback with the Red Sox, went 1-for-3.
Corey Brown, who replaced Sizemore in center, drilled a long solo homer to right-center off Tampa Bay's Santiago Garrido in the eighth.
Up next: The Rays will throw Opening Day starter David Price and closer Grant Balfour in Tuesday's 1:05 p.m. ET game -- a free exclusive audio webcast at rays.com -- against the Twins at home in Port Charlotte, Fla. Ricky Nolasco and Scott Diamond are expected to pitch for Minnesota.
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. This story was not subject to the approval of Major League Baseball or its clubs.