Indiana took a 60-48 lead into the fourth quarter, but the Sky stormed back with a 14-3 run to open the final period and pulled within one. Allie Quigley had five points during the burst, including the lone 3-pointer made by the Sky.
Chicago then missed its next six shots allowing Indiana to build separation as Zellous hit a pair of 3's to put the game away.
Sylvia Fowles led Chicago with 20 points and 14 rebounds. Elena Delle Donna and Quigley added 14 apiece.
Indiana trailed Chicago only in the first two minutes of the game.
Game 2 will be in Chicago on Monday.
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