ST. PETERSBURG, Fla. -- The Boston Red Sox have won eight of their last 10 games, and their pitching has held opponents to three runs or fewer in seven of those eight wins, building momentum as the postseason nears.

"We know that we're in these final couple of weeks with something very real and tangible within our reach, and guys are putting it out on the line every night," Red Sox manager John Farrell said after a 3-1 victory over the Tampa Bay Rays on Saturday night. "That's the driver. They all have to go out and pitch well."

The Tampa Bay Rays, closing out a three-game series with Boston on Sunday, are in a different position, only barely lingering on the outside of a logjam wild-card race in the American League. Two straight home losses and seven of the last nine have dropped them to 72-77 -- they are 5 1/2 games behind the Minnesota Twins -- and motivation is running out.

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"It's as frustrating as you get," pitcher Alex Cobb said of a second straight close home loss Saturday night. "To have two tough losses like that, coming back home, it doesn't get any harder to handle."

The first-place Red Sox lead the stubborn New York Yankees by three games in the American League East.

Boston on Sunday turns to left-hander Eduardo Rodriguez, who is 5-5 with a 4.19 ERA but dominated the Rays in his last start against them, striking out a career-high 13 batters late last season. He's pitched well of late, allowing a total of three runs while pitching six innings in each of his last two starts while holding opponents to a .171 batting average.

Rodriguez is still seeking his first win against the Rays in four career starts, carrying a 7.58 ERA in those games.

The Rays close out the series with right-hander Jake Odorizzi (8-8, 4.52 ERA) on the mound. Odorizzi didn't make it out of the fourth inning Monday, getting to 94 pitches and giving up five runs (one earned) and three hits in the inning in a loss to the Yankees.

Odorizzi has struggled against Boston this season, going 0-2 with a 7.71 ERA in three starts. In his last start against the Red Sox on Aug. 9, he left after four innings when he suffered a right foot contusion. For his career, he's 2-2 with a 3.08 ERA at Tropicana Field against Boston, and 3-5 with a 4.56 ERA against Boston overall.

The Rays get Monday off but then have the Cubs and former manager Joe Maddon in for two games midweek, so there's little margin for error and less time to make up ground as they cling to slim hopes of staying in contention.

Saturday's game was close enough that a sixth-inning balk provided the margin of victory, and a close call on a potential third strike set up what was the winning runs for the Red Sox.

"You could tell from the reaction of the guys coming up that it was a big pitch, we needed the pitch and it was unfortunate," Tampa Bay manager Kevin Cash said. "It's tough to say one pitch decides the outcomes of games, but they can really swing the momentum one way or another, and ultimately that one did."