Mora hit a solo homer in the second inning, a two-out RBI single in the third and snapped a 4-4 tie with a two-out single in the fifth. In addition to his sparkling performance at the plate, the third baseman also made an outstanding catch of a foul bunt by Ian Kinsler in the eighth inning.
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 for the AL wild card.
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.
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, Elvin 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.
Danys Baez worked the eighth and Jim Johnson got three outs for his eighth save.
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 broke a four-game losing streak and improved to 15-33 since the All-Star break.
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 and decisive 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. 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. Elvis 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.
Baltimore tied it in the bottom half. After Nolan Reimold hit a solo homer, Millwood loaded the bases with three walks and Mora singled off the glove of third baseman Esteban German.
Notes
Millwood has allowed five runs in three of his last four starts. … 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.