Cano hit a 2-2 pitch from Randy Williams (0-1) into New York's bullpen in right-center, delighting what was left of a soggy crowd at Yankee Stadium. Williams retired the first two batters he faced before walking Hideki Matsui and Nick Swisher on four pitches apiece to set up Cano's first game-ending homer.
Brian Bruney (4-0) worked a perfect 10th inning for the win. Cano was batting just .176 with two outs and runners in scoring position this season before his clutch hit.
Derek Jeter hit his second leadoff homer this week and Johnny Damon also connected for AL East-leading New York, which won the opener of the three-game set despite leaving nine runners on base.
Mark Buehrle pitched six effective innings for the White Sox but remained winless in seven starts since his perfect game against Tampa Bay on July 23. The All-Star lefty is 0-4 with a 5.77 ERA over the lackluster stretch.
Sliding Chicago has lost five of six to fall five games behind AL Central-leading Detroit, which beat Tampa Bay 6-2.
The White Sox rallied in the seventh against CC Sabathia, who tied a season high with 10 strikeouts and was in line to become the first pitcher in the majors to reach 16 wins before he tired in his last inning. Alex Rios doubled in a run and Gordon Beckham lined a two-out RBI single into right to tie it at 2.
Ramon Castro tried to score on Beckham's hit but Nick Swisher cut him down at the plate for the final out. Third baseman Alex Rodriguez also made two nice plays in the inning, throwing Carlos Quentin out at home on Castro's grounder and diving to his right to keep Jayson Nix's hit in the infield.
Sabathia received a no-decision after winning his previous 11 August starts. The big left-hander still finished up this month with a 5-0 record and a 2.64 ERA.
Jeter hit a 1-2 pitch from Buehrle over the wall in left-center for his 22nd career leadoff homer and first since Sunday's 8-4 win at Boston. It was his 17th homer this season and career No. 223, passing Don Mattingly for 10th on the club's list.