Paxton (2-0), coming off a win over Tampa Bay in his big-league debut last week, yielded only two hits. The 24-year-old left-hander walked two and struck out five, throwing 65-of-97 pitches for strikes.
Danny Farquhar pitched a scoreless ninth for his 14th save as the Mariners evened the three-game series.
Franklin Gutierrez knocked a two-run double, scoring Paxton and Dustin Ackley to break a scoreless tie in the fifth.
Kendry Morales added a solo homer for Seattle.
Michael Wacha (3-1) surrendered two runs on four hits over five innings for St. Louis, which fell into a first-place tie with Pittsburgh atop the National League Central.
Wisconsin business offering 'therapeutic cuddling' forced to close
Workers accuse National Zoo of animal mismanagement