When Jose Mesa finished his complete-game, 9-2 victory, the Orioles had outscored Texas, 31-14, in the series to take a five-game winning streak on the road.
That is the Orioles' hottest surge since last September.
Mesa was practically unhittable while establishing a career strikeout high with nine and rolling behind a big offensive splurge.
Chito Martinez and Leo Gomez both homered for the Orioles, combining to drive in seven runs.
With the Rangers facing another doubleheader in Cleveland tonight and their bullpen in need of a reprieve, Oil Can Boyd was forced to take a beating for the club.
The Orioles crunched him for 12 hits in the first four innings and roared to a 9-1 lead that eased Mesa's return from the minors.
Boyd, who spent most of the season with Montreal, wound up with a club record for hits allowed as his record went to 0-4 with the Rangers.
Kevin Reimer gave Texas a short-lived 1-0 lead with a first-pitch homer off Mesa in the second, but Mesa retired the next 14 Rangers in order while the Orioles pounded away.
Martinez got the balls flying with a two-run homer in the bottom of the second after a walk to Randy Milligan. That tied Martinez for the major-league lead among rookies with eight.
It didn't last long. In the next inning, after Martinez had knocked in a run with a bases-loaded fielder's choice, Gomez took over undisputed possession of the rookie lead with his ninth home run.
His three-run shot into the left-field bleachers gave the Orioles a 7-1 cushion and sent them to their first four-game sweep since last season.
The onslaught continued in the fourth with two more runs, Martinez knocking in a fourth run with an infield single. That rally ended with Joe Orsulak trying to advance to third base on the play following an overthrow by Steve Buechele.
Manager John Oates simply wanted Mesa "to do the same thing he did in his last start." That was a six-hit shutout for Rochester against Richmond last Saturday.
"I want him to make the pitches when he has to and gain confidence," said Oates. "When he was sent down he couldn't get out of innings. He has to throw more than just fastballs."
Mesa had faced the Rangers only once before, dropping a 1-0 duel to Nolan Ryan in April. He pitched seven innings and allowed the run on Rafael Palmeiro's sacrifice fly.
The start was his first since June 28 when he lasted only two-plus innings and lost to Boston, 9-3.
He was winless in his previous nine starts, going 0-5 with an 8.29 ERA. His previous victory with Baltimore was May 11.
The Rangers had lost four straight and six of seven overall and seven of their last nine games on the road.
Texas offered no semblance of an offensive threat after Reimer's homer. Its only baserunners were on two walks to Palmeiro and he never advanced beyond first base.
The second hit Mesa allowed came in the eighth inning, a leadoff single by Dean Palmer.
Rangers second: Reimer homered to right on 0-0 count. Buechele popped out to shortstop C.Ripken. Palmer popped out to second baseman Bell. Rodriguez grounded out to shortstop C.Ripken. 1 run, 1 hit, 0 errors, 0 left on. Rangers 1, Orioles 0.
Orioles second: Milligan walked. Martinez homered to right center on 0-0 count, Milligan and Martinez scored. Gomez tripled down the left field line. Hoiles struck out. Bell grounded out to second baseman Buechele. Devereaux singled to left, Gomez scored. Anderson grounded out to shortstop Hernandez. 3 runs, 3 hits, 0 errors, 1 left on. Orioles 3, Rangers 1.
Orioles third: C.Ripken singled to right center. Orsulak singled to right, C.Ripken to second. Milligan walked, C.Ripken to third, Orsulak to second. Martinez grounded into fielder's choice, second baseman Buechele to shortstop Hernandez, C.Ripken scored, Orsulak to third, Milligan forced at second. Gomez homered to left on 1-1 count, Orsulak, Martinez and Gomez scored. Hoiles grounded out to third baseman Palmer. Bell struck out. 4 runs, 3 hits, 0 errors, 0 left on. Orioles 7, Rangers 1.
Orioles fourth: Devereaux doubled to left. Anderson popped out to catcher Rodriguez. C.Ripken singled to center, Devereaux scored. Orsulak singled to right, C.Ripken to third. Milligan struck out. Martinez singled to second, C.Ripken scored, Orsulak to second, Orsulak out advancing, catcher Rodriguez to third baseman Palmer. 2 runs, 4 hits, 0 errors, 1 left on. Orioles 9, Rangers 1.
Rangers eighth: Hulett to second base, batting 3rd. Segui to first base. Bell to shortstop, batting 9th. Palmer singled to left center. Petralli, pinch hitting for Rodriguez, grounded out to first baseman Segui, pitcher Mesa covering, Palmer to second. Hernandez singled to center, Palmer scored, Hernandez to second on throw home. Downing popped out to right fielder Orsulak. Stanley flied out to right fielder Orsulak. 1 run, 2 hits, 0 errors, 1 left on. Orioles 9, Rangers 2
Site: Milwaukee County Stadium
Orioles starter: Dave Johnson (3-4, 8.20)
Brewers starter: Don August (8-5, 4.81)
Radio: WBAL (1090 AM), WTOP (1500 AM)
TV: Channels 2, 20