Former Mariners reliever Matt Thornton (2-1) was dominant. The White Sox left-hander had five strikeouts in 2 1-3 innings for the victory.
With two outs in the ninth, Jones, who turned 33 Friday, came back from an 0-2 to count to homer off Mariners reliever Mark Lowe (1-2) into the left field bullpen.
Jose Lopez hit his first career grand slam in the seventh inning for the Mariners who lost for just the second time in nine games.
White Sox starter Gavin Floyd was unable to hold a 5-2 lead in the seventh inning, loading the bases before J.J. Putz relieved. After an out, Lopez homered.
The Mariners bullpen failed to hold the lead in the seventh when Rios greeted Brandon Leaugue with an RBI double to make it 6-all
Milton Bradley was back in Chicago and although he was out of the lineup with a sore calf, Bradley met with the Chicago media before the game for the first time since his 2009 season ended when the Cubs suspended Bradley after a verbal altercation with their hitting coach, and after he criticized the atmosphere of the organization.
Bradley told a Chicago TV station that he felt misrepresented by the media.
"As a black man playing this game, I just don't feel like ... you know, the majority of the media is middle-aged white guys, so I don't think you can accurately construe what I have to say, or portray me as who I am, because you don't know," Bradley told Chicago Comcast Sportsnet.
Bradley called himself a "nerd" and said he plays scrabble with Mariners reliever Shawn Kelly in the bullpen.
If and when Bradley plays during the three-games series, he doesn't care what kind of reception he gets from the Chicago fans.
Mariners starter Ryan Rowland-Smith pitched 5 1-3 inning and allowed five runs
- three earned - on six hits.