BOSTON -- The Tampa Bay Rays are far behind in the playoff race. Manager Joe Maddon still has high hopes, especially with his starting pitchers beginning to get on a roll.

David Price worked eight crisp innings and the Rays held the Boston Red Sox to three hits for the third straight game, winning 4-0 on Wednesday and gaining confidence about making a charge in the tough AL East.

The Yankees led the Red Sox by one game and the Rays by nine going into New York's game at Kansas City on Wednesday night.

"The possibility of a really good run is there," Maddon said. His pitchers "are feeding off one another right now. Everybody's trying to do the topper thing and I'm good with that."

The combined shutout by Price and Kyle Farnsworth followed a day-night doubleheader in which James Shields and Jeff Niemann each pitched a complete game. Boston beat Shields in the opener 3-1 before Niemann struck out 10 in a 6-2 victory in the nightcap.

Boston's streak of three straight home games with three hits or less is a franchise first, the team said, citing research by the Elias Sports Bureau. It's the first time the Rays have pitched three consecutive three-hitters.

Had he been told before the series that the Rays would hold the Red Sox down like that, "I would have been very happy," Price said with a laugh. "I'd hope the first guy gave up five and the next guy gave up four. The last one none."

Boston is second in the majors with a .277 batting average but is hitting just .168 in 11 games against Tampa Bay.

"When you play in this venue or the new Yankee Stadium, that venue, it should draw the best out of you," Maddon said. "It's like a salve or an ointment. It should pull it out there and that's what I think happens to us."

B.J. Upton and Evan Longoria homered as Tampa Bay won for the seventh time in nine games. Boston lost for the fifth time in its last seven.

"It's been our whole thing not to give up," Upton said. "There's still a lot of baseball left to play. We play the Yankees and the Red Sox (14 more) times."

Price entered with just two wins in his previous nine starts and losses in three of his previous four decisions. Then he completed the trio of three-hitters.

"To pitch three games like that?" Maddon said. "Come on. I never envisioned that."

Boston had a few chances, but couldn't come up with a big hit.

"We've been swinging the bats so well," said Boston designated hitter David Ortiz, who missed all three games with bursitis in his right heel. "It's frustrating. Everybody on this ballclub is a big part of what we have here. When anybody is out of the lineup, you can feel it."

Dustin Pedroia singled with one out in the first and Adrian Gonzalez walked to put runners on first and second. But Price got Kevin Youkilis to ground into a double play.

Jacoby Ellsbury, who hit two homers on Tuesday, led off the sixth with a triple to deep right-center field. Pedroia struck out and Ellsbury was tagged out in a rundown when Gonzalez tapped back to Price. Gonzalez ended up at second before Youkilis grounded out.

"Ells hit the three-run homer" in Tuesday's opener, Red Sox manager Terry Francona said. "Other than that, we didn't do much. Price was good, changing velocity, good breaking ball. A lot to like if you're not in this uniform."

The Rays jumped on the Red Sox in the first. Johnny Damon hit a one-out single and took second when right fielder Darnell McDonald let the ball get by him for an error. Damon took third on a wild pitch by John Lackey (11-9) and scored on a groundout by Ben Zobrist.

Upton hit a leadoff drive to left in the fourth for his 17th homer and Longoria went deep in the fifth, belting a two-out drive to left on a 3-0 pitch for his 19th of the season.

Lackey pitched a perfect sixth but was knocked out in the seventh when Zobrist hit a two-out RBI double. Kelly Shoppach, who had been hit by a pitch for the second time in the game, scored on the play.

With the way the Rays are pitching, that was plenty.

"It's crunch time for us," Shields said, "and to be able to pitch like that in a three-game series gives us a lot of confidence going forward."

Game notes

Damon's second-inning double was his 2,670th career hit, moving him ahead of Gary Sheffield and into 64th place. ... Ellsbury stole his 32nd base in the third and is tied for third place in team history with Carl Yastrzemski at 168. ... Tampa Bay is off Thursday before starting a three-game series at home on Friday night against the Seattle Mariners. Wade Davis (8-7, 4.60 ERA) pitches for the Rays against Felix Hernandez (11-10, 3.38 ERA). ... Josh Beckett (9-5, 2.40) pitches for the Red Sox on Thursday night when they open a four-game series at Kansas City. Luke Hochevar (8-9, 4.89) goes for the Royals. Beckett was 6-0 in his career against the Royals before losing his last outing against them on July 28. ... Lackey was 6-0 in his previous seven starts, the best winning streak of his career.