Trailing 3-2 in the sixth, Tyler Flowers -- who came into the game in the third inning after starting catcher A.J. Pierzynski was ejected by home plate umpire Lance Barrett for arguing balls and strikes -- socked a solo homer to tie the score.
Alexei Ramirez followed with a double to chase Mariners starter Blake Beavan (8-8). Charlie Furbush relieved and induced Jordan Danks to ground out, sending Ramirez to third.
One out later, Wise lined a solid single to center, scoring Ramirez for a 4-3 Chicago lead.
Ramirez drove in Alex Rios with an eighth-inning sacrifice fly for what proved to be the decisive run.
Nate Jones (6-0) earned the victory after working out of a two-on, two-out jam in the top of the sixth. Addison Reed picked up his 24th save for the American League Central-leading Chisox.
Kyle Seagar belted two homers to account for all four Seattle runs as the Mariners lost to the White Sox for the 18th time in 21 meetings.