Four more K's pushed the total to 48 as the game stretched into the 18th inning, making it MLB's longest of the season by innings and duration. It also was the first interleague game to go 18 innings and the longest in game time, at 6 hours, 5 minutes, in the history of Sunday Night Baseball, since the series began in 1990.
"It's just a crazy game," Yankees manager Joe Girardi said.
Starlin Castro drove in Hicks with a fielder's choice in the 18th for the go-ahead run.
"We're going to grind out games," Hicks said. "We're going to fight to the end."
Hicks led off with a bunt single against Strop (0-2) and advanced to second when the Cubs' catcher, Contreras, threw it into right field for an error. With one out and Hicks on third, Castro hit a bouncer up the middle. Russell tried to throw home, but it was wide, and Hicks scored easily.
"I know we lost, but you've got to try to have fun with it," Rizzo said.
Before Hicks scampered home with the winning run, the biggest highlight of extra innings belonged to Schwarber. The Cubs' slugging left fielder went into the stands in foul territory for an outstanding catch on Headley's foul popup in the 12th.
"Tremendous play," Cubs manager Joe Maddon said.
What was left of the crowd also sung along when the Cubs showed a tape of Harry Caray singing "Take Me Out To The Ball Game" for the second seventh-inning stretch in the 14th.
The Yanks (20-9) completed a three-game sweep of the Cubs (16-15) for their first sweep of a defending champion on the road since doing the same to the 2003 Angels. New York also moved to 11 games over .500 -- equivalent to the most games over .500 that the Yanks were all of last season (the last time on Sept. 10).
Chicago trailed 4-1 before it rallied in the ninth against Aroldis Chapman, who helped the Cubs win the World Series last year for the first time since 1908. Albert Almora Jr. and Javier Baez each singled in a run before Chapman hit the slumping Rizzo on his left wrist with the bases loaded on his 36th pitch, forcing home the tying run.
Rizzo got an X-ray on his arm and it came back negative.
"Thank my parents I drank my milk when I was a kid," Rizzo said. "Decent bones."
"I felt normal. It just wasn't my night tonight," Chapman said through a translator.
Information from The Associated Press and ESPN Stats & Information was used in this report.