Lowe (1-0) didn't allow a hit or a walk after entering the game with two out in the second inning.
Tepesch had to leave after taking a line drive off his right wrist. He was diagnosed with contusion and is expected to make his next start.
Joe Ortiz, Tanner Scheppers and Jason Frasor finished up the shutout for the Rangers, who have outscored Seattle 12-0 in taking the first two contests of a three-game series.
Mariners starter Brandon Maurer (1-3) absorbed the loss, surrendering two runs on two hits over 6 2/3 frames.
'Happy' fan videos make Pharrell cry [VIDEO]
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend