Just like that, the White Sox were celebrating. And the Yankees were dealing with another brutal loss.
"I think everybody right there before the hit was thinking, here we go again," Beckham said. "We claw our way back in the game, just to lose it in the 12th."
Instead, it was the Yankees wondering how this one got away. That wasn't the biggest story, though.
The Rodriguez saga took another turn, two days after he was hit with a 211-game punishment following MLB's investigation into Biogenesis of America, a defunct Florida anti-aging clinic accused of distributing banned performance-enhancing drugs.
The players' union formally appealed the suspension, sending the case to an independent arbitrator.
They're 11 1/2 games out of first place, a stunning number for a team that hadn't been 10 or more games off the lead since Sept. 17, 2008
The White Sox rallied with two out in the bottom half against Adam Warren (1-2).
Tyler Flowers singled off the pitcher's glove and moved to third on a single by Alexei Ramirez. De Aza followed with a triple to right-center, giving the White Sox their third straight win after a 10-game losing streak.
"I was just trying to hit the ball hard," De Aza said. "Anywhere, hit the ball hard. If I hit it, something could happen."
Beckham, who had homered earlier in the game, he knew the game was over as soon as the ball left De Aza's bat.
"He (De Aza) hit that ball in the gap," Beckham said. "I think everyone knew it was going to score two. Great swing. He killed that ball. Just a great win. It was fun."
The Yankees looked like they were going to come away with the win when Cano broke out of a 6 for 43 slump by driving a pitch from Dylan Axelrod (4-8) 431 feet to right-center. The home run -- his 22nd -- was his first since July 10.
The Yankees built an early 4-0 lead and were up one going into the ninth, but Rivera couldn't hold it.
Baseball's all-time saves leader, came in to a standing ovation and retired the first two batters before Gordon Beckham doubled.
A pinch-hitting Adam Dunn then drove a single just to the left of a diving Rodriguez at third on an 0-2 pitch to tie it at 4.
The blown save was just the third in 38 opportunities for Rivera, who allowed one run over two innings. And it denied CC Sabathia his first win in more than a month after he pitched into the eighth.
"You don't expect to tie it up off the greatest closer ever, but I guess with our team that makes perfect sense," Chicago's Paul Konerko said, smiling.
Rodriguez picked up a single and walked in his third game back after having hip surgery in January. He also had a chance to drive in the go-ahead run with two out in the 11th but grounded out with a runner on third. Then, he was replaced in the field in the bottom half.
Alfonso Soriano hit a two-run homer off Hector Santiago and scored twice. Eduardo Nunez went deep and collected three hits, and Sabathia was in line for his first win since July 3 before things turned.
He gave up three runs and five hits, including a towering homer to Beckham in the fifth.
The White Sox pulled within 4-3 in the seventh on an RBI double by Konerko and fielder's choice grounder by Beckham, and Sabathia left after Conor Gillaspie grounded out leading off the eighth.
David Robertson came in and struck out Tyler Flowers looking on a 3-2 pitch, drawing an argument from the White Sox player and an ejection for pitching coach Don Cooper in the dugout.
Alexei Ramirez then singled and stole second, but De Aza grounded out to end the inning.
Santiago struggled, allowing four runs and seven hits over 5 2/3 innings, but the bullpen kept the White Sox in the game.
Austin Romine started his second straight game at catcher for the Yankees. Girardi said there is nothing wrong with Chris Stewart. ... Dayan Viciedo was back in the White Sox's lineup as the designated hitter -- not the left fielder -- after missing a game because of a jammed left thumb. ... Both teams are off Thursday. ... The White Sox have a day-night doubleheader against Minnesota on Friday, with LHP John Danks starting the first game and LHP Charlie Leesman making his major league debut in the nightcap. ... RHP Ivan Nova starts Friday for the Yankees, with RHP Rick Porcello pitching for Detroit.