Ernesto Frieri struck out Texas slugger Josh Hamilton with the bases loaded for the game's final out to clinch the Angels' 3-2 win on Saturday.
Los Angeles southpaw C.J. Wilson and Rangers starter Yu Darvish (7-3) engaged in a pitchers' duel before giving way to their respective bullpens.
Frieri, who recorded the final out in the eighth, gave up a leadoff single to Mike Napoli in the ninth, the first hit allowed by the right-hander in 13 1/3 innings as an Angel.
Ian Kinsler worked a two-out walk and Elvis Andrus reached when shortstop Erick Aybar's throw pulled first baseman Albert Pujols off the bag. But Frieri fanned Hamilton to earn his fourth save of the season.
"Those guys can swing the bats," Frieri said. "I was relaxed. I thought I made really good pitches to Hamilton."
The Angels have won 10 of their last 11 games, while Texas has dropped a season-high four straight.
Wilson did not factor into the decision despite scattering five hits over six scoreless innings. The former Ranger walked three and struck out five.
Rangers center fielder Craig Gentry reached over the wall to rob Aybar of a homer leading off the third.
The Angels opened the scoring in the bottom of the sixth, capitalizing on a pair of defensive miscues. Pujols reached second on Napoli's fielding error, stole third and scored on a misplay by Adrian Beltre.
Texas loaded the bases with nobody out in the seventh and pinch-hitter David Murphy hit a game-tying sacrifice fly off winning pitcher Bobby Cassevah (1-0).
The Angels retook the lead with two runs in the home seventh. Alberto Callaspo singled home Aybar and Kendrys Morales added a sac fly.
Mike Trout, who reached on an infield hit and stole second, scored on a close play at the plate. Right fielder Nelson Cruz caught Morales' fly ball before throwing a strike to the plate and Trout was called safe by umpire Tim McClelland. Rangers catcher Yorvit Torrealba was ejected for arguing.
Texas got a run back in the eighth when Andrus led off with a walk and advanced to third on a two-out single by Michael Young. Right fielder Torii Hunter's errant throw to third enabled Andrus to score.
"This is uncharacteristic Rangers baseball," Murphy said. "We know we're a better team than this. We can't give games away. We need to play good baseball."
Darvish gave up three runs -- two earned -- on five hits, walked three and struck out seven in 6 1/3 innings...The Rangers have lost four straight and seven of their last nine to AL West teams...Beltre struck out four times to snap his hitting streak at 10 games.