Darvish was pushed back a day to give him extra rest with an eye toward pitching in the NL wild-card round, but the Padres lost their third straight game. With Milwaukee's win over Miami, their magic number remained at three for clinching a wild-card berth.
The Padres' lead over Philadelphia for the No. 2 wild card was cut to 1 1/2 games and they're just two games ahead of the Brewers with five to play.
The Padres struck out 15 times.
The White Sox, eliminated from the playoff chase a year after winning the AL Central, won for the second straight day after losing eight straight.
Darvish (16-8), who was trying for his career-best 17th win, had his six-start winning streak snapped. He allowed three runs and eight hits in six innings, struck out six and walked one.
Darvish allowed consecutive singles opening the second before retiring the side.
He wasn't as lucky in the fourth, when he allowed three hits in an inning for the first time in six starts to allow the White Sox to take the lead. Jiménez hit a leadoff homer to left, his 16th. Gavin Sheets doubled to center and scored the go-ahead run on Yoán Moncada's single to right.
The White Sox made it 3-1 in the sixth when Moncada hit a one-out double to right and scored on Andrew Vaughn's single.
White Sox rookie Davis Martin (3-5) held San Diego to one run and six hits in 5 2/3 innings, struck out a career-best eight and walked none.
Liam Hendricks pitched a perfect ninth for his 35th save.
San Diego's Brandon Drury was knocked down when he was hit on the bill of his helmet by a pitch from Martin with one out in the fourth. Drury was checked by a trainer and remained in the game.
Drury was placed on the seven-day concussion list on Sept. 5 after being hit on the face flap of his helmet by a pitch from Dustin May of the Los Angeles Dodgers on Sept. 2.
Drury doubled with one out in the second and scored on Josh Bell's single.
- Home Plate Umpire - Mike Muchlinski
- First Base Umpire - Dan Merzel
- Second Base Umpire - Ryan Wilson
- Third Base Umpire - Steve Jasinski