The White Sox (36-120) had taken a 2-1 lead on home runs by Korey Lee and Miguel Vargas off Yu Darvish, but that lead quickly disappeared in the eighth.
This defeat came a day after the White Sox tied the American League record of 119 losses set by the 2003 Detroit Tigers.
The 1899 Cleveland Spiders hold the major league record for losses at 20-134.
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The Padres (90-66) clinched their first 90-win season since 2010, when they finished 90-72 but missed the postseason thanks to a brutal September collapse.
The Padres reduced their magic number to one for clinching their third postseason berth since 2020.