Juan Pierre went 3-for-4 with a trio of steals and three runs scored for Chicago, which won the final three contests and has triumphed in seven of its last eight games. Dayan Viciedo, making his first career start at first base, added a two-run homer off Lester in the fifth.
John Danks (15-11) allowed five hits and two runs over six innings. The lefty fanned six batters and extended his career-high for wins in a season.
Lester (19-9) was pounded for nine hits and eight runs over four-plus frames. The southpaw also walked five batters, fanned five and had his personal six- start winning streak snapped.
Victor Martinez ripped a two-run homer for Boston, which finished 43-38 on the road and will head home to host the playoff-bound Yankees this weekend to conclude the season.
Pierre singled and stole two bases in the opening inning before scoring on a Jones base hit.
Martinez homered to left in the third with Marco Scutaro on base in the top of the third, but Chicago tied the game in the bottom half when Jones singled in Pierre.
Alejandro De Aza doubled with one out in the fourth, Pierre and Alexei Ramirez walked with two down to set up Konerko's ninth grand slam of his career, a blast to left field. It was his 39th homer of the season.
Ramon Castro singled in front of Viciedo's homer to right in the fifth to account for the final margin.
The teams had to be pulled off the field with one out in the bottom of the sixth due to a power outage. The game was delayed 21 minutes.
The White Sox host Cleveland this weekend...Danks has allowed two earned runs or less in 21 starts this season...The White Sox finished 6-1 against Boston this year. It marks their most victories against the Red Sox since 1998 (6-5)...Sergio Santos had three strikeouts in two innings for Chicago. That brought the White Sox's bullpen to 435 strikeouts for the year, equaling the 2009 club record for most strikeouts by a relief corps.