Vargas, one of four candidates for Seattle's fifth starter spot, allowed two hits, walked one and struck out one in 3 2-3 scoreless innings. The 27-year-old left-hander threw 49 pitches while becoming the first Mariners pitcher to get into the fourth.
Vargas has allowed three hits in 5 2-3 shutout innings this spring.
Aaron Laffey pitched two scoreless innings for Cleveland, and Wes Hodges had a pair of two-run doubles.
Franklin Gutierrez hit a two-out, two-run triple in the fourth for Seattle.