Jennings hit his first homer of the spring with a leadoff blast in the third inning off O's starter Wei-Yin Chen and followed it up with a two-out grand slam the following frame.
"I felt good from the first at-bat, I felt like I was seeing the ball good and I was swinging at good pitches today," Jennings said. "I felt like I was swinging the bat good. I was swinging at pitches in the zone. Hitting them on the barrel and getting to pitches inside, that's a good sign for me."
The Rays hit Chen hard, capitalizing on shortstop J.J. Hardy's fourth-inning error to extend the inning and load the bases for Jennings. Evan Longoria, who doubled in his first at-bat, gave the Rays their third homer of the day with a solo shot in the fifth before Jennings struck again in the top of the seventh off Kevin Gregg.
"They're a great team. They have great hitters and they hit me well with my fastball," said Chen through his interpreter.
Rays Opening Day starter James Shields cruised through four innings, throwing 60 pitches as planned. He allowed only Hardy's homer in the first and picked up six strikeouts in his final spring tuneup. Shields ends the Grapefruit League season 3-0 with a 2.08 ERA.
Hardy homered twice for the Orioles, going deep off Rays reliever Matt Torra to open the sixth. Nick Markakis added a solo home run of his own in the eighth inning.
Chen, who is expected to be part of Baltimore's rotation, struggled all afternoon. The 26-year-old lefty allowed a first-inning run and Jennings seemingly had his number with a pair of long balls. Hardy's error didn't help things and Chen exited after five innings having allowed seven runs (three earned) on six hits and two walks.
Lefty Zach Phillips pitched a 1-2-3 sixth in relief of Chen, making a nice defensive play to retire Reid Brignac for the third out. Nick Johnson added a solo homer off Torra in the bottom of the seventh.
Up next for the Orioles: The O's will play their first of two college games, facing Florida Southern on Monday in a game that will be pitched on both sides by Orioles relievers. The game is open to fans by paid admittance with first pitch scheduled for 7:05 p.m. ET.
Brittany Ghiroli is a reporter for MLB.com. Read her blog, Britt's Bird Watch, and follow her on Twitter @britt_ghiroli. This story was not subject to the approval of Major League Baseball or its clubs.