Jennings cruised effortlessly into second base and scored one out later when Evan Longoria, who had minor surgery to his left hamstring in the offseason, doubled to right. The Rays' All-Star third baseman also ran easily as Tampa Bay took a 1-0 lead.
Oswaldo Arcia led off the Twins' second with a double to right off Rays starter Roberto Hernandez. He scored when Joe Benson grounded to shortstop Yunel Escobar, who made a bad throw to first. Jeff Clement followed with a single to center that scored Benson to give the Twins a 2-1 lead.
Luke Scott, who had missed a week's worth of games with a tight left hamstring, tied the score at 2 with a solo home run off Worley to lead off the Rays' second.
Arcia singled to start the Twins' fourth and scored on Darin Mastroianni's sacrifice fly to give the Twins a 3-2 lead.
Longoria added his second RBI double of the game in the fifth.
Hernandez, who is competing for the No. 5 spot in the rotation, allowed three runs -- two earned -- on five hits and struck out three in four innings.
"I felt great today," Hernandez said. "I kept the ball down. ... I'm very, very happy about [the way I'm progressing]. Every day I continue to work."
Worley allowed two runs on five hits and a walk while striking out two in four innings.
Up next: Alex Cobb will make his fourth start of the spring Tuesday afternoon, when the Rays host the Yankees in a 1:05 p.m. ET contest at Charlotte Sports Park. Cobb, who is penciled in as the Rays' No. 4 starter, has allowed just two earned runs in nine innings thus far and has struck out 12. Brandon Gomes and J.D. Martin are also scheduled to see action. Ivan Nova is scheduled to start for the Yankees.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.