Perez (2-1), making his third start of the season, gave up six hits over 6 2/3 innings as part of the Rangers' second straight shutout.
Derek Holland blanked the New York Yankees on two hits in a complete game Thursday. Texas had shut out the Yankees in the final two innings of an 8-5 win Wednesday.
The Rangers won their third in a row and have captured nine of 11.
Cincinnati, which has dropped three straight, suffered the loss of starting pitcher Johnny Cueto after just one inning. He left the game with a strained muscle in his throwing shoulder, having already spent a month on the disabled list this year.
Cueto (4-2) gave up a two-out, RBI single to Adrian Beltre in the first.
Tony Cingrani relieved Cueto and walked four batters in the second inning, two of them with the bases loaded.
Jurickson Profar singled home the final Texas run in the fifth. The contest was the opener of a nine-game Texas homestand.