Chicago led 2-1 entering the ninth, but Sale (2-2) allowed a leadoff double to Kelly Johnson and a single to David Cooper. With one out, he intentionally walked J.P. Arencibia, before issuing free passes to Mark Teahen and Adam Loewen, giving the Blue Jays a 3-2 advantage.
Sale's implosion capped a tumultuous final week for the White Sox (79-83), who parted ways with longtime manager Ozzie Guillen on Monday.
Shawn Camp (6-3) tossed a scoreless eighth inning to earn the win for the Blue Jays (81-81), who avoided a three-game sweep.
Frank Francisco stranded a runner at second in the ninth to record his 17th save.
The White Sox, playing under interim manager Don Cooper, built a 2-1 lead behind a strong start from Philip Humber. Over 6 2/3 innings, Humber allowed just one run on two hits while registering a career-high nine strikeouts.
"I definitely think that we have plenty of talent in this clubhouse," said Humber. "I've been saying that all year but it just didn't work out for us this year."
Toronto starter Brandon Morrow lasted six innings, surrendering two runs on five hits. He walked five and fanned seven.
The Blue Jays took a 1-0 lead in the first on Mike McCoy's leadoff walk and Eric Thames' subsequent double.
The White Sox left the bases loaded in the home first, but tied the game in the fourth on Gordon Beckham's two-out blast to left.
They grabbed the lead in the fifth, when Alejandro De Aza began the inning with a single and scored on Alexei Ramirez's double down the left field line.
After the first inning, Humber did not allow another Blue Jay to reach scoring position. He left following Teahen's two-out single in the seventh. Matt Thornton struck out Jose Molina to end the inning and tossed a scoreless eighth before handing the ball to Sale for the ninth.
Cooper served the last nine full seasons as the White Sox pitching coach. He signed a four-year extension Tuesday to remain with the club...On Wednesday, Chicago announced the resignation of hitting coach Greg Walker...Guillen signed a four-year contract to manage the Florida Marlins on Wednesday...The Blue Jays won the season series, 4-3.