Paulino (3-6) allowed only two hits, didn't issue a walk and struck out 11 Mariners in a dominating performance that gave the Royals their first win in a four-game set in Seattle.
Greg Holland hurled a scoreless eighth and Joakim Soria notched his 27th save to wrap up the victory for the Royals.
Hosmer's blast capped a three-run first inning and Jeff Francoeur added a solo shot in the ninth for Kansas City.
Seattle's Michael Pineda (9-10) absorbed the loss, yielding three runs on five hits over eight innings.
Mike Carp and Justin Smoak clubbed solo homers for the Mariners.