The win was the Cubs' first World series victory in Chicago's Wrigley field since October 8, 1945.
The Cubs, who were facing elimination, now trail 3-2 as the World Series shifts back to Cleveland for Game 6 on Tuesday.
The Indians' early lead was erased when Kris Bryant led off the bottom of the fourth with Chicago's second home run of the series.
Joe Maddon called on Chapman to get the final eight outs of Game 5 Sunday night, a move that paid off in the form of a 3-2 Cubs win over the Indians that now sends the World Series back to Cleveland, reported the New York Daily News. The lefty has pitched five innings in the series and allowed only one hit.
The 28-year-old left-hander, known for his record 169kph fastball and strikeout skills, shut down Cleveland rallies in the seventh and eighth innings as the Cubs edged the Indians 3-2 and pulled within 3-2 in Major League Baseball's best-of-seven final.
"That was a big ask and he answered", Indians manager Terry Francona said of Chapman. Cleveland closed within a run in the sixth when Rajai Davis singled, stole second scored on a two-out single by Francisco Lindor, who is hitting.421 in the Series.
Josh Tomlin will start Game 6 on short rest against Jake Arrieta, and if he can't finish the job for the Indians, they still have an ace up their sleeve.
The Chicago Cubs are climbing a mountain and they were reluctant to give up the ghost in Game 5 by extending the series.
Aroldis Chapman usually never works much more than an inning as Chicago Cubs closer. With the designated hitter rule back in play for Game 6, Schwarber will return to the Cubs' lineup as they try to force a winner-take-all Game 7. If they deliver the same strong pitching and patient, timely hitting, we could be looking at a potentially unforgettable seven-game series.
The Cubs trailed 1-0 before scoring three times in the fourth.
"If Chappy had covered first base, there would have been a lot less angst going on", Maddon said.
"I don't know that we could do what we did (Sunday), necessarily", Maddon said of Chapman.
Jon Lester got the start for Chicago and responded to the pressure by striking out the side in the first inning. Heyward planted his foot and grabbed the top of the wall, then reached back toward the field with his glove to snag the ball. But how about Jason Heyward and his highlight-reel catch on Trevor Bauer's foul fly down the right-field line in the third inning? "You can't have the mindset of going out there and trying to win the game in the first inning".
"We're always confident", Rizzo said.
"I'm feeling unbelievable", said Cubs fan Nicole Herrington, 29, moments after her team won.