Tepesch (1-0), a rookie out of the University of Missouri, allowed four hits while striking out five, retiring 12 consecutive hitters at one point.
The right-hander became the first Ranger to pitch into the eighth inning in his major league debut since John Dettmer in 1994.
Rays starter Roberto Hernandez (0-2) gave up six runs (five earned) on eight hits over 6 2/3 innings.
Desmond Jennings supplied two hits for Tampa Bay, which dropped a third straight.
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