"These big games, I love to have them," Cobb said. "They really make me focus in a lot more."
Cobb (6-2) lost his shutout bid when Brett Gardner homered leading off the ninth and he wound up allowing two runs and five hits in 8 1/3 innings with eight strikeouts.
"The young man knows how to pitch," Yankees manager Joe Girardi said. "He's got one of the best changes, split-change, whatever you want to call it in the game."
Nix reached on an infield single in the third, when replays showed he appeared to be out. He was New York's only runner until Robinson Cano grounded a single to center leading off the seventh.
Cobb allowed three hits over 8 1/3 innings in a 3-0 victory over Andy Pettitte on April 24.
"He was wonderful," Tampa Bay manager Joe Maddon said. "He was that good."
Sabathia (4-4) dropped to 0-2 with a 4.85 ERA since he beat Toronto on April 27. He allowed seven runs and seven hits in seven innings and is 10-11 in 31 starts against the Rays, including a 3-10 mark since joining the Yankees. His overall ERA is 3.96.
"I'm hurting the team," Sabathia said. "Not being able to make pitches with two strikes, fastball command. I feel fine. It's just one of those things where I feel like the ball is coming out pretty good, but I'm just not making pitches."
Sabathia's career-high streak for consecutive winless starts is six, from July 3-Aug. 1, 2002, and March 31-April 27, 2003, according to STATS.
"He's missing some pitches and he's not getting away with it," Yankees pitching coach Larry Rothschild said. "Every mistake he made, they hit it. Early in the season, he had the same velocity and pitched really well. He was just executing pitches better."
"You put up eight runs against the Yankees, definitely something good, but the 'W' is all that matters," Rodriguez said.
New York, which won the first two games of the series, came up short in the bid for its first sweep of three or more games at Tropicana Field since Sept. 13-15, 2005.
Tampa Bay took a 2-0 lead in the second after Rodriguez was hit by a pitch, Adams made a high throw to second when he tried for a forceout on Yunel Escobar's grounder to third and Escobar beat first baseman Lyle Overbay's throw to second on Loney's grounder, a play in which Sabathia failed to cover first. Jose Lobaton hit a broken-bat RBI single to center and Sam Fuld followed with a sacrifice fly.
Rodriguez homered in the third for a 4-0 lead. His only other home run this year was April 24 off Pettitte.
Escobar hit an RBI double in the sixth and scored on Loney's homer. Desmond Jennings added an eighth inning RBI double.
Sabathia is 3-7 in 16 starts at Tropicana Field, which is his lowest winning percentage in any current major league ballpark. ... The Yankees are at the New York Mets on Monday, which marks the start of closer Mariano Rivera's final regular season Subway Series. "We've played a lot of good games at our place and good games at their place," said Rivera, who says he is retiring after the season. ... Tampa Bay RHP Jake Odorizzi (0-0) will make his second start in place of injured Cy Young Award winner David Price (left triceps strain) Monday against Miami.