Ichiro Suzuki had a two-run single and the Yankees rallied for their fourth straight victory following a 2-7 slide. Chasing an American League playoff spot, they finished a 4-2 homestand against two losing teams by getting their second game-ending hit against Chicago in three days.
Avisail Garcia hit a tying homer in the ninth for the White Sox, who have lost a season-high six in a row and dropped their last eight games at Yankee Stadium.
New York rallied for four unearned runs off All-Star ace Chris Sale in the sixth to take a 4-3 lead, capitalizing on an error by left fielder Dayan Viciedo.
Toronto took advantage of an error and an infield single to put runners at the corners with none out in the bottom half, but Jose Reyes and Cabrera popped out before Boxberger ended it by fanning Nolan Reimold.
Tampa Bay opened the scoring in the first when Zobrist doubled and scored on Longoria's fielder's choice.
It stayed that way until the seventh, when Toronto broke through against Rays right-hander Chris Archer. Juan Francisco's sacrifice fly got Toronto on the board.
Rays manager Joe Maddon, who protested Saturday's game over the timing of a replay challenge by Blue Jays manager John Gibbons, was booed when he came out for a successful challenge on a fielder's choice first base in the fifth.
Maddon was booed again when he came out but declined to challenge a call at second base in the seventh, and tipped his cap to the crowd of 38,869 as he walked back to the first base dugout.
Blue Jays outfielder Jose Bautista went 0 for 3 and was ejected by home plate umpire Bill Welke for arguing after being called out on strikes in the sixth. Bautista, who is hitless in 11 at-bats, failed to reach base in three consecutive games for the first time since April 9-11, 2012. Reimold replaced Bautista.
It was the fifth ejection of the season for Toronto but the first for a Blue Jays player.
Rays: OF David DeJesus (broken left hand) went 1 for 2 with two walks and a stolen base in a seven-inning stint with Class-A Charlotte on Saturday night, while C Ryan Hanigan (left oblique) went 0 for 4 as the DH.
Rays: Tampa Bay begins a four-game series at AL East-leading Baltimore on Monday, with RH Jake Odorizzi facing Orioles RH Chris Tillman (10-5). Odorizzi is 4-0 with a 2.45 ERA in his past five road starts.