Garza allowed one run in eight innings for the Tampa Bay Rays in another sparkling performance against the Orioles, and Brignac and Bartlett also contributed heavily Monday night in a 5-1 victory.
The game drew 9,129 fans, the smallest crowd in the 19-year history of Camden Yards.
Carl Crawford went 4 for 4 with a homer for the Rays, who played their first road game of the season in their favorite stadium away from home.
Garza (2-0) gave up six hits, struck out five and walked three in beating the Orioles for the second time this season. The right-hander is 8-1 lifetime against Baltimore, including 5-0 with a 3.00 ERA in six career starts at Camden Yards.
Bartlett doubled in the third to extend his hitting streak at Camden Yards to 17 games, and Brignac homered and drove in two runs. He's 6 for 10 with two homers and five RBIs lifetime in Baltimore.
"I love playing here. I love this ballpark," Brignac said. "It's a beautiful park. I hit the ball well here, but it's just circumstance as far as the home run was concerned."
After Felix Pie gave Baltimore a 1-0 lead with a first-inning shot, Brignac tied it in the third with his second career homer. The other homer, of course, was at Camden Yards.
"Goodness sakes, we can't get him out," Orioles manager Dave Trembley lamented.
Baltimore fell to 1-6 with its fourth straight loss. The Orioles have scored only 20 runs this season, including three in their last three games.
Asked if he might shuffle a lineup that includes slumping Adam Jones (.233), Nick Markakis (.143) and Miguel Tejada (.207), Trembley said, "Yeah, I may do something, maybe just to show a different look."
Garza yielded hits to four of the first six batters he faced, then kept the Orioles hitless until Ty Wigginton singled with two outs in the seventh. Earlier in the inning, Crawford made a fine diving catch of a liner to left by Garrett Atkins.
"For me, the play of the game was Crawford making that catch," Trembley said.
Orioles starter Jeremy Guthrie (0-2) allowed three runs and eight hits in seven innings. He's 2-7 lifetime against Tampa Bay, 0-2 this season after twice going up against Garza.
"I've had two starts and been outpitched twice by Matt," Guthrie said. "I deserve to be 0-2, and that's where I am."
Crawford hit his first home run of the season in the eighth off Mark Hendrickson, and Brignac drove in a ninth-inning run with a 30-foot single down the third-base line.
Pie gave the sparse crowd a thrill by hitting Garza's second pitch over the center-field wall. It was the first career leadoff homer for Pie, who is getting a tryout atop the batting order in place of the injured Brian Roberts.
"When he gave up the leadoff run that didn't bother me, because I knew he would settle down," Tampa Bay manager Joe Maddon said of Garza. "It wasn't a great effort, but it was good and efficient."
Brignac tied it in the third. Later in the inning, Bartlett doubled and was thrown out by Pie trying to score on Crawford's single to left.
The Orioles placed Roberts on the 15-day disabled list and recalled INF Justin Turner from Triple-A Norfolk. ... Zobrist has both triples allowed by the Orioles this year. ... Markakis received his AL-leading 10th walk.