ST. PETERSBURG, Fla. -- Alex Cobb set the tone for a big game with his breaking ball.
Cobb (3-3), who had lost his previous three starts, struck out a career-high 10, walked one and hit a batter. He gave up only Gaby Sanchez's third-inning ground single to center until Greg Dobbs had a two-out single in the seventh.
"Today was, like, the uncanny ability first-pitch curveball strike," Tampa Bay manager Joe Maddon said. "You put that in the hitter's head, then combine that with the great changeup, fastball where he wants to. He was really, really good."
In his three losses, Cobb allowed 14 runs in 18 2/3 innings.
"I felt great the last three outings, Cobb said. "(This) turned out to be one of my better outings."
"You can not win games with two base hits ... nothing going on," Marlins manager Ozzie Guillen said. "Seems like when you're not scoring and you're not hitting, I don't saying we are, feels like flat."
"I'm not saying they're not trying, I'm not saying they don't care, they do. We all do," Guillen added. "But make hitting simple. See the ball, hit the ball and have some fun playing baseball. Just be aggressive."
Tampa Bay rookie Matt Moore and two relievers combined on a one-hitter in an 11-0 win over the Marlins on Friday night.
Upton put the Rays up 1-0 on a first-inning leadoff homer. It was his first home run since May 22.
Josh Johnson (4-5) allowed two runs and eight hits in six innings for the Marlins, who have dropped 10 of 12. He had gone 4-1 over his previous seven starts.
"Lots of balls ... struggled to find the zone," Johnson said. "I was all over the place. I found a way to battle and get outs."
Johnson threw just 55 of 108 pitches for strikes. The loss was his first interleague defeat since June 23, 2007, against Minnesota, a stretch that included six wins in nine starts before Sunday.
The teams were coming off a 15-inning game Saturday night that lasted 5 hours, 7 minutes and was won 4-3 by the Marlins.
"We had really good energy about us under the circumstances," Maddon said. "I could feel it in the dugout, and Alex really permitted that to happen."
Josh Johnson got defensive help in the third when Sanchez made a nice grab at first base on Hideki Matusi's liner with runners on first and third and turned it into an unassisted inning-ending double play.
The Rays had two on with one out during the fourth, but Johnson worked out of the jam by striking out Sutton and Sean Rodriguez. The right-hander also got a one-out double-play grounder from Matusi one inning later with two runners on.
Matsui went 1 for 15 during the three-game series.
The Rays optioned RHP Brandon Gomes to Triple-A Durham. ... Tampa Bay OF Matt Joyce was a late scratch because of flulike symptoms. ... Marlins LHP Mark Buehrle (5-7), who has 24 interleague wins, will face Boston RHP Clay Buchholz (7-2) in the opener of a three-game series Tuesday night at Fenway Park. ... Rays RHP Kyle Farnsworth (strained right elbow) is scheduled to pitch with Class-A Charlotte for the third time on Monday night. ... Tampa Bay starts a nine-game road trip Tuesday night at Washington.