Kurt Suzuki drove in three runs for the Twins, who won two of three for their first road series win against the Rays since September 2006.
''In this ballpark, you never feel safe,'' Twins manager Ron Gardenhire said. ''We basically threw everything at them we had.''
Gardenhire moved past Chuck Dressen into sole possession of 59th place on the career victory list with 1,009.
Fuld, claimed off waivers from Oakland on Sunday, had two hits in his Twins debut Wednesday and added three more Thursday. He spent the previous three years with the Rays.
''It's nice to come back and contribute,'' Fuld said.
After having a four-run lead cut to one, Minnesota went ahead 8-3 in the fifth on a run-scoring double by Fuld and Hicks' shot off reliever Heath Bell. It was Hicks' first homer since July 14 against New York Yankees ace CC Sabathia.
''He was excited,'' Gardenhire said. ''It's good to see. You knew it was going to be one of those kind of games. The guys came out and scored some runs, and then we just hold on.''
Ricky Nolasco (2-2) allowed six runs and 10 hits over six-plus innings. Glen Perkins pitched the ninth for his fifth save.
The Twins were coming off a 6-4, 12-inning win over the Rays Wednesday that ended at 11:58 p.m.
''We've been battling,'' Nolasco said. ''A long game last night. Guys came back ready to go today.''
Erik Bedard (0-1) gave up four runs, five hits and five walks in four innings. It was the eighth time in 10 games that Tampa Bay's starter went five or less innings.
''Early on he just kept missing,'' Rays manager Joe Maddon said. ''It wasn't like he was throwing the ball badly, but he kept missing inside. But 90 pitches after four (innings), I like the fact that he got that deep.''
The Twins took a 3-0 lead in the first with the help of four walks and two hits off Bedard. Suzuki had a two-run single and Fuld hit an RBI double.
James Loney drove in the first of his two runs with a double before David DeJesus got the Rays within 4-3 on a two-run homer in the second. After seventh-inning sacrifice flies by Desmond Jennings and Matt Joyce, Tampa Bay cut the deficit to 9-7 in the eighth on pinch-hitter Logan Forsythe's RBI single off Jared Burton.
Bell departed after Suzuki's RBI infield single went off his leg in the sixth.
Juan Carlos Oviedo, coming back from elbow ligament replacement surgery, replaced Bell and went 1 1-3 scoreless innings in his first major league appearance since Sept. 21, 2011, with Miami when he was known as Leo Nunez.
NOTES: Fuld got a nice ovation before his first at-bat Wednesday. When asked before Thursday's game about Fuld being back in the lineup, Gardenhire smiled and said ''the fans are like they want to see him, so we'll play him.'' ... Minnesota C Joe Mauer and Hall of Famer Dave Winfield will co-host the Players Trust All Star Golf Tournament at Windsong Farm Golf Club in Independence, Minn., on July 16 to raise funds for area children's charities. ... Twins RHP Kevin Correia (0-2) and Detroit RHP Rick Porcello (2-1) will pitch in the opener of a three-game series Friday night. ... Tampa Bay begins a four-game series Friday night at the Chicago White Sox with RHP Chris Archer (2-1) going against RHP Erik Johnson (1-1).