Jonathan Papelbon, making his first appearance in eight days, pitched a scoreless fifth.
Phillies left-hander John Lannan started and allowed four runs on five hits, including the Rodriguez homer, with three strikeouts in four innings. He has a 5.00 ERA this spring.
The Rays got things going when Jose Lobaton reached on an infield single to lead off the third. Shawn O'Malley then ripped a ball off the third base bag to put runners on first and second with one out. Desmond Jennings singled to left, but Phillies left fielder Domonic Brown had the ball roll underneath his glove. Both Lobaton and O'Malley scored to make it 2-0.
The next batter, Rodriguez, punctuated the inning with a two-run shot to left.
Lobaton added a sacrifice fly in the sixth to score Ryan Roberts and make it 5-1.
Yuniesky Betancourt's sacrifice fly in the bottom of the inning scored Brown, and then Humberto Quintero and Ben Revere added two-out RBI singles to close the lead to 5-4. Revere went 3-for-4 to up his spring average to .351.
The Rays added four runs in the seventh on Leslie Anderson's fielder's choice, Robinson Chirinos' RBI walk and Hak-Ju Lee's two-run single to make it 9-4.
Laynce Nix and Quintero added RBI singles in the bottom of the inning for the Phillies to make it 9-7. Quintero went 3-for-4 with three RBIs.
The Rays added six runs in the eighth. Anderson had a two-run single and Chirinos followed with an RBI double before Shelley Duncan blasted a two-run homer to make it 14-7.
Cole Figueroa capped the scoring with a run-scoring single to make it 15-7.
Rays right-hander Jeff Niemann allowed a run on four hits and struck out three in 3 2/3 innings. He gave up his only run in the fourth on Howard's homer.
Up next: The Phillies head east to play the Houston Astros at 1:05 p.m. ET on Sunday afternoon in Kissimmee, Fla. The game can be watched live on MLB.TV. Left-hander Cole Hamels is scheduled to start. Also slated to pitch are Zach Miner, Tyler Cloyd, Justin De Fratus, Ethan Martin and Jonathan Pettibone. De Fratus is a top candidate for one of the three remaining bullpen jobs. He got roughed up in his first two Grapefruit League appearances, but his last two have been scoreless.