The Rays stayed 1 1/2 games behind the first-place New York Yankees in the AL East and extended their wild-card lead over Boston to seven games. Tampa Bay has won five of six and nine of 12.
Garza (14-7) gave up one run and five hits in 5 2/3 innings. It was an extension of an outstanding August in which he had a 1.27 ERA over five starts.
In his last outing against the Orioles, Garza yielded four homers and seven runs in 6 1/3 innings. The right-hander's performance in the rematch provided a measure of redemption and improved his lifetime record against Baltimore to 9-1, including 3-0 this season.
Rafael Soriano worked the ninth for his major-league leading 41st save.
Felix Pie drove in the lone run for the Orioles, mired in their first three-game losing streak under manager Buck Showalter. Baltimore is 17-13 since Showalter made his debut on Aug. 3.
Kevin Millwood (3-15) allowed four runs and seven hits in 5 2-3 innings. He was vying for a second straight win after going nine straight starts without one.
Millwood allowed at least one first-inning run in 13 of his previous 17 starts, and it appeared the trend would continue when Crawford hit a two-out triple and Evan Longoria walked. But Carlos Pena popped out to end the threat.
In the third, however, Crawford hit an RBI single and scored on Longoria's AL-high 43rd double.
Reid Brignac singled in a run and Ben Zobrist hit a sacrifice fly to make it 4-0 in the fourth. Baltimore got a run back in the bottom half when Ty Wigginton doubled, advanced on a wild pitch and scored on a fly ball to center by Pie.
Garza was lifted in the sixth after issuing two walks. Chad Qualls came in and got Matt Wieters to ground out.
Notes
The Orioles intend to call up RHP Chris Tillman and start him Sunday in the series finale. Baltimore will go with a six-man rotation to preserve the arms of rookies Jake Arrieta and Brian Matusz. … Longoria is four doubles short of breaking Aubrey Huff's season team record (47 in 2003). … Baltimore's Nick Markakis went 0 for 4, ending his season-high hitting streak at 11 games. … The victory evened manager Joe Maddon's record at Tampa Bay at 391-391, the first time he's been at .500 since the Rays were 8-8 on April 20, 2006. … Tampa Bay improved to 10-3 against Baltimore and won the season series for a third straight year.