Perez (4-3) allowed four hits and four walks but struck out seven in notching his first victory in nearly a month.
Jason Frasor and Neal Cotts combined for 1 2/3 scoreless relief innings and Joe Nathan tossed a 1-2-3 ninth for his 33rd save as second-place Texas posted a triumph in the first of a three-game series.
The victory pulled Texas within two games of American League West-leading Oakland.
The Rangers trailed 1-0 in the fifth when they loaded the bases with two outs and David Murphy scored the equalizer on a wild pitch by Angels starter Jerome Williams.
Andrus then lofted a fly ball to short right field that second baseman Howie Kendrick got a glove on before colliding with right-fielder Collin Cowgill. The ball rolled free and two runs scored as Andrus ended up at third.
Kendrick was helped off the field with a hyperextended left knee and is listed as day-to-day.
Williams (5-8) yielded five runs on six hits over 5 1/3 innings.