Volstad pitched six solid innings to stop a personal six-game winless streak and the Marlins got two RBIs from rookie Mike Stanton in a 6-1 victory over the Rays on Sunday.
"It was good to win a series, especially against record-wise the best team in baseball," Volstad said. "We're playing great right now. Let's keep it going."
Volstad (4-6) gave up one run and four hits, struck out three and walked four. He was 0-4 with a 4.91 ERA in six starts since earning a win against Washington on May 7.
Tampa Bay first baseman Carlos Pena was hitless in four at-bats, ending his streak of six games with at least one homer. He finished two games shy of the major league record shared by Dale Long (Pittsburgh 1956), Don Mattingly (New York Yankees 1987) and Ken Griffey Jr. (Seattle 1993).
"That is really cool, no doubt about it, I was very happy to be mentioned among those players," Pena said.
The Rays dropped into a tie for first in the AL East with the New York Yankees, who beat Houston 9-5 Sunday. Tampa Bay had held sole possession of first for the past 51 days.
"We expected all those teams to be in it the whole entire time," Rays center fielder B.J. Upton said. "We're not going to change a thing. If we keep playing the baseball we know how to play and how we've been playing it, things will end up working out our way."
Boston and Toronto are also in contention for the AL East title.
Rays right-hander Jeff Niemann (6-1) allowed five runs and nine hits over six innings. He was 8-0 in 16 starts at home since losing to Boston on May 2, 2009.
"Just a lack of execution on my part," Niemann said. "They didn't miss any mistakes."
The Marlins scored four times in the sixth to take a 5-1 lead. Cantu went deep, Stanton hit an RBI single and Helms added a two-run shot.
Stanton, a highly touted prospect, also singled in a run with two out in the fourth. Through his first five games since joining the Marlins from Double-A Jacksonville on Tuesday, Stanton is hitting .368 with four RBIs in five games.
"Pretty productive," Stanton said. "I'm learning a lot, still. I'm fine with it. There's always room for improvement but I'm satisfied for the first week. Just keep pushing forward."
The Rays tied it at 1 in the bottom half on Ben Zobrist's sacrifice fly, which was caught by second baseman Dan Uggla. With Uggla running away from the infield, Carl Crawford easily beat his spinning throw to the plate.
Tampa Bay loaded the bases with one out in the fifth, but Volstad got grounders from Crawford and Evan Longoria to stave off the threat.
"I think that's an inning he can grow up on and get better," Marlins manager Fredi Gonzalez said. "I hope he learned from that and keeps getting better."
Helms hit his first homer since Sept. 2 in Saturday's 6-5 loss to the Rays. ... Marlins LHP Nate Robertson, moved to the bullpen due to a rainout and off day, will return to the rotation and start Friday's game against Tampa Bay. ... Crawford hit into a first-inning double play. It ended his stretch of 239 at-bats without grounding into a DP. ... Florida LHP Renyel Pinto (strained left hip) is expected to be activated from the 15-day disabled list on Tuesday. ... Tampa Bay 2B Sean Rodriguez had three hits and has a career-best 14-game hitting streak. ... Cantu has a hit in 12 straight games.