It was the ninth straight Chicago victory, its longest winning streak in almost two years.
The White Sox were a game below .500 when they embarked on the streak with a shutout of Minnesota May 23. Chicago has won 13 out of 14.
Gordon Beckham hit a two-run homer in the first and added a solo shot in the fifth while the White Sox were building a four-run lead.
The Mariners then bounced back to tie the contest, getting a two-run homer by Kyle Seager in the seventh and an RBI single from Seager during a two-run eighth.
After A.J Pierzynski was walked intentionally, Lillibridge raced in with the go-ahead run on the single by Ramirez. Orlando Hudson next drew a walk to load the bases and Alejandro De Aza drove in two runs with a single.
Jesse Crain (1-0) recorded the final two outs in the eighth to pick up the win. Addison Reed worked around a hit in the ninth for his seventh save.
All three Chicago runs in the eighth were unearned, but they cost Shawn Kelley (0-2) the loss.
Swim Week Miami Beach 2014 [PHOTOS]