Wolf (1-1) earned his first win of the season after surrendering just one run on three hits while striking out seven batters.
Wolf's previous win in the majors came on September 22, 2012 as a member of the Baltimore Orioles in a 9-6 win over the Boston Red Sox.
"Randy was great tonight," said Marlins manager Mike Redmond. "It was a tremendous effort, exactly what we needed."
Casey McGehee drove in two runs and Ed Lucas had two hits for the Marlins, who rebounded after being swept in three games by the Braves.
Desmond Jennings went 2-for-4 with an RBI and Sean Rodriguez scored for Tampa Bay, which has lost seven straight.
Alex Cobb (1-3) gave up three runs -- all in the first inning -- on five hits with two walks and five strikeouts in defeat.
The Marlins opened the scoring in the first. Christian Yelich walked, Lucas singled and Giancarlo Stanton was also issued a free pass to load the bases. McGehee's single up the middle brought in two runs and Stanton scored when Garrett Jones grounded into a double play.
Rodriguez walked to lead off the fifth and raced home on Jennings' RBI double down the left-field line to make it a 3-1 game.
After running into trouble in the first, Cobb settled down to retire 13 straight batters and allowed just two baserunners the rest of the way, but Tampa Bay's offense could not get anything going.
Steve Cishek, who took the loss after giving up two runs in the ninth on Sunday, retired the Rays in order to earn his 12th save of the season.