Josh Tomlin (7-1) lasted 3 2/3 innings and lost for the first time since Sept. 15. The right-hander was 12-0 in 13 starts following a Cleveland loss dating back to last season.
Desmond, the game's second batter, gave Texas a quick lead with a homer into the left-field bleachers. Mazara, who is having an impressive rookie season, hit his ninth homer to dead center during a four-run fourth.
Elvis Andrus was 3 for 4 with an RBI and has hit safely in 28 of 29 career games at Progressive Field
Texas, which leads the AL West, has won eight of 10.
Indians manager Terry Francona was ejected in the third inning by plate umpire Manny Gonzalez. Francona argued that the Rangers' Mitch Moreland should have been called out for running inside the baseline while going to first base after hitting a ground ball. Moreland was hit in the back of the helmet by a throw from Tomlin, allowing a run to score and giving Texas a 4-0 lead.
Francona came on the field and had a lengthy discussion with Gonzalez. He was ejected after he went back to the dugout, and then returned to the field for a heated argument with the umpire.
Tomlin was charged with eight runs, four of which were unearned thanks to his own throwing error in the third and Uribe's double error in the fourth.
Austin Adams relieved Tomlin and allowed Mazara's home run.
Holland, who broke a three-game losing streak, gave up six hits and struck out two. Cesar Ramos pitched the final three innings for his first save.
Rangers: OF Shin-Soo Choo (strained left hamstring) is taking batting practice and continuing a running program in Arlington.
Indians: RHP Carlos Carrasco (strained left hamstring) could rejoin the rotation this week. He threw a bullpen session Monday.
Rangers: RHP Colby Lewis (4-0) is seeking the first 5-0 start of his career. He was the winning pitcher against the Angels on Wednesday despite allowed a season-high six runs in five innings, his shortest outing of the season.
Indians: RHP Corey Kluber (4-5) has won his last start two starts and looks to even his record. He allowed three earned runs over 14 innings, beating the Red Sox and White Sox.