Tampa Bay failed to give AL All-Star David Price any run support.
After Price pitched eight shutout innings, Taylor Teagarden broke out of a long slide with an RBI double in the 10th that led the Baltimore Orioles over the Rays 1-0 on Sunday.
Tampa Bay has been held scoreless for 21 innings over more than two games.
"We just can't hit right now," manager Joe Maddon said.
Price, bidding for his 15th win of the season, allowed two hits, struck out five and walked three.
"Every time you play somebody in the AL East, it's going to be a pretty good game," Price said.
Joel Peralta (1-4) walked Mark Reynolds with one out in the 10th and threw a called third strike past Omar Quintanilla. Teagarden, in a 1-for-25 slide, lined a two-out drive to left-center.
Luis Ayala (3-3) got three outs in the ninth, and Jim Johnson finished for his 32nd save in 35 chances as both teams pitched three-hitters.
Baltimore has won 10 consecutive one-run games dating to June 22, and 11 straight extra-inning contests.
Baltimore's Miguel Gonzalez scattered two hits over seven innings, struck out four and walked four.
"Gonzalez threw the ball extremely well," Price said. "It was just a good game."
In his only other start against the Rays, Gonzalez allowed seven runs in 2 2-3 innings of a 10-1 loss on July 25
Price got some help in the second from right fielder Matt Joyce, who made a nice over-the-shoulder running catch on Teagarden's two-out drive with two on.
Tampa Bay second baseman Ben Zobrist left after three innings because of upper-back spasms and was replaced by Will Rhymes. The injury was not thought to be serious.
"He seems fine," Maddon said. "More than likely he's going to be OK on Tuesday. So it's one of those fortunate things."
NOTES: The Rays are off on Monday before starting a three-game series Tuesday night against Toronto. ... Rays RHP Jeff Niemann (broken right fibula) threw off a bullpen mound and is scheduled to make his first minor league rehab start Wednesday for Class-A Charlotte. ... Tampa Bay DH Luke Scott (right oblique) has resumed onfield batting practice. ... Rays closer Fernando Rodney extended his scoreless stretch to 21 innings — which ties Joe Borowski's 2005 team record for a reliever — after not allowing a run in the ninth. ... The Rays held their first bark in the park event, with approximately 450 dogs in attendance. A section in left field was reserved for dog owners and their pets.