ST. PETERSBURG, Fla. -- It was only one series for the Rays and one start for right-hander Alex Cobb, but Tampa Bay's 4-1 victory over the New York Yankees on Wednesday at Tropicana Field capped a promising beginning to the 2017 season.

Cobb (1-0), working his way back from 2015 Tommy John surgery, held the Yankees to one run on four hits in 5 2/3 innings, helping the Rays take two of three in the opening series from New York.

"Awesome series win," manager Kevin Cash said. "Today obviously was special for Alex to get out there and do his thing. He looked good ... great performance by him, great performance by our bullpen and the defense played really, really well behind them."

Tampa Bay got all its scoring in the first two innings, getting five hits in the second off New York starter Michael Pineda (0-1), who didn't make it out of the fourth inning and gave up eight hits, extending a streak from last year to 11 straight starts without a win.

"He made some mistakes with his fastball," manager Joe Girardi said, pointing to the lack of two-out success. "It looked like he was going to get out of that inning without giving up a run, and he just couldn't seem to get the third out."

The big hits came from the top and bottom of the Rays' lineup. Corey Dickerson led off the first with a home run and added an RBI single in the second, with No. 9 hitter Derek Norris bringing in the other runs with a two-out single in the second. Tampa Bay's bullpen threw 3 1/3 innings of scoreless relief, with Alex Colome pitching the ninth for his second save of the season.

The Yankees got the leadoff man in the ninth when Jacoby Ellsbury singled off Colome's glove, but Starlin Castro grounded into a double play. Chase Headley, continuing a strong start to his season, also singled off Colome's glove, but Aaron Judge popped out to center to end the game.

The Yankees get their second day off in four days before opening a three-game series at Baltimore. The Rays stay home to open a four-game series against Toronto on Thursday night.

For the second time in three games, the Rays jumped on a Yankees right-handed starter, tagging Pineda for three runs on five singles in the second inning for a 4-1 lead.

The two teams traded solo home runs early, with Dickerson leading off the bottom of the first with his first of the season and Ellsbury answering in the second.

The Rays struck back in the bottom of the second, however, with Steven Souza leading off with a single and Logan Morrison following with a single that caromed off one of the stadium's catwalks. The Yankees got an out at the plate after a wild pitch put runners at second and third, but with two outs, Norris ripped a two-run single that took a bounce past second baseman Castro's glove for a 3-1 lead.

"You believe in him, but you've got to get those outs. Those are the big outs that you have to get," Girardi said of Pineda's struggles.

Norris stole second base -- the first steal by a Rays catcher since Ryan Hanigan in Sept. 2014 -- and the move paid off as he scored on an RBI single by Dickerson to make it 4-1.

"I really take a lot of pride in two-out RBIs," Norris said. "When a pitcher gets a big out, I think they have a tendency to relax a little bit, almost like they're off the hook. Getting that big knock, those are swing runs, especially early in the game. I think that really swung the game in our favor."

Cobb, who had an 8.59 ERA last season in limited work, pitched well in his season debut, holding the Yankees to one run on three hits in the first five innings while striking out four batters.

Pineda lasted only 3 2/3 frames, giving up four runs and eight hits while striking out six batters.

Tampa Bay took an early lead in Sunday's opener off Yankees righty Masahiro Tanaka but managed little offense in a 5-0 loss Tuesday against left-hander CC Sabathia.

NOTES: INF/OF Nick Franklin, designated for assignment by the Rays on Saturday, was claimed Wednesday by the Milwaukee Brewers. ... Tuesday's 5-0 Yankees' victory marked the first time in Rays' history that they were shut out by six or more pitchers in a nine-inning game. It was the third time in Yankees history they've used six or more pitchers in a nine-inning shutout ... The Rays are 69-64 against the Yankees since the start of 2010 -- the only American League team with a winning record against New York in that span -- after going 69-133 in their first 12 seasons from 1998-2009. ... Despite the 1-2 record, the Yankees have gotten strong pitching from their bullpen, with 13 2/3 innings of scoreless relief over the three games. RHP Adam Warren had 2 1/3 innings Wednesday, after getting 2 1/3 scoreless innings in Sunday's loss.