The 37-year-old Mora hit a solo homer in the second inning, a two-out RBI single in the third and snapped a 4-all tie with a two-out single in the fifth. Along with his sparkling performance at the plate, the third baseman made an outstanding catch of a foul bunt by Ian Kinsler in the eighth inning.
Mora, the longest tenured player on the team, is in the final year of his contract with Baltimore and nearing the end of a down season. But on this day, he carried the Orioles offensively.
"I think my motivation is when you see the other team in the other clubhouse, they're contending for the playoffs," Mora said. "When you see guys play like it's the playoffs, that comes into my body. I'm going to play like it's the playoffs, too."
Matusz was appreciative of his teammate's performance.
"Mora came up very clutch today with some two-out hitting, and the home run obviously was huge," the pitcher said. "He just swung the bat really well."
Making his seventh big league start, Matusz (4-2) allowed four runs and six hits in seven innings. The left-hander faced the minimum 12 batters over his final four innings; the lone batter to reach, Elvis Andrus on a walk, was thrown out trying to steal.
The 22-year-old Matusz struck out four and walked one. He's 3-0 over his last four starts.
"I feel great right now. I feel strong. I've conditioned myself really well and I feel healthy," he said.
The Orioles donned replica uniforms of the 1949 Baltimore Elite Giants, who won the Negro League championship 60 years ago. To keep with the spirit of the occasion, the players and coaches wore stirrups.
Matusz and Mora were more of a factor than the clothes they wore, but the Orioles nevertheless improved to 15-33 since the All-Star break.
David Murphy homered for the Rangers, denied their first five-game winning streak since July 19-24. Texas did not get a hit after the third inning and remained two games behind Boston (which lost to the White Sox) for the AL wild card.
"Things didn't change. We're still in the same spot," Rangers manager Ron Washington said. "We still have to come back [Sunday] and do what we wanted to do anyway -- win the series."
Kevin Millwood (10-9) gave up five runs, seven hits and four walks in five innings. He has won only two of his last 11 starts.
"I just pitched bad. I don't know what to say," the right-hander said. "I thought pitch selection was bad, location was bad."
Baltimore took a 5-4 lead in the fifth when Nick Markakis got an infield hit, went to second on a hit-and-run groundout and scored on Mora's two-out single up the middle.
It turned out to be the final run in a game that featured plenty of early offense.
A run-scoring double by Marlon Byrd and a two-run homer by Murphy gave Texas a 3-0 first-inning lead, but Matusz didn't panic.
"I knew after the first inning that I had good stuff. I could feel it in the bullpen and going out to the mound," he said.
Markakis hit a sacrifice fly in the bottom half, and Mora's seventh homer got Baltimore within a run in the second.
Texas made it 4-2 in the third. Andrus was credited with a triple when his liner to right was lost in the sun by Markakis, and Byrd followed with a sacrifice fly. Matusz avoided further damage by retiring Ivan Rodriguez with runners on second and third and two outs.
Texas OF Josh Hamilton rejoined the team but missed a second straight game with a back injury. ... Batting third for the second straight game, Baltimore's Brian Roberts went 0 for 3 and is 7 for 46 (.152) since Aug. 23.