Josh Hamilton went 2 for 3 with a two-run home run and three RBIs in support of Yu Darvish, who won for only the second time in six starts in an 8-3 victory against the Tigers on Sunday at Rangers Ballpark in Arlington.
Darvish (12-8) tied a Rangers rookie record for wins in a season, while allowing three runs on six hits and five walks in 6 2/3 innings.
Hamilton, who extended a hitting streak to 10 games with a two-run home run in the first, also reached base on a walk.
Robbie Ross recorded the last out in the seventh and bullpen mates Michael Kirkman and Tanner Scheppers pitched scoreless eight and ninth innings.
The Rangers struck quickly. Elvis Andrus reached on an infield single and was soon around the bases on Hamilton's 32nd home run that brought home RBIs 97 and 98 on the season.
Errors led to two unearned runs in the third.
Mitch Moreland led off the inning and scored on a double by Ian Kinsler, who took third on the throw home. Andrus, the next batter, hit a comebacker to Rick Porcello, who appeared to have caught Kinsler off third.
But Porcello's throw to the bag was low and away, darting past third baseman Miguel Cabrera and down the right-field line. Hamilton followed with his third RBI of the game, a single that left him on third when Brennan Boesch let the ball run under his glove and to the wall.
Darvish found trouble in the fifth after walking leadoff Alex Avila, who was followed by Jhonny Peralta's single and a run-scoring double from No. 9 hitter Omar Infante.
Darvish struck out the next two hitters, Austin Jackson and Andy Dirks, before Cabrera connected on a two-run double.
Consecutive two-out walks in the seventh precipitated a change by Washington, who went to lefty Robbie Ross to face Prince Fielder.
A night after walking Fielder to set up a potential big inning, Ross retired him on Sunday with a fly ball out to left fielder David Murphy.
The Rangers added two runs in the seventh with the help of three Tigers wild pitches.
Darvish joined Chris Young, Kevin Brown and Edwin Correa as Rangers rookies who won 12 games as rookies.
Rick Porcello took the loss and fell to 8-7.