Trailing 80-78 with 19 seconds left, Ionescu took the ball and drove the lane where she was fouled by Rebekah Gardner.
Ionescu, who finished with 17 points, nine assists and eight rebounds, converted the free throw to give New York (10-17) the lead.
Chicago (21-7) got the ball but Candace Parker missed a shot in the lane with just over 2 seconds left. After Michaela Onyenwere hit two free throws, the Sky had one last chance, but Emma Meesseman's 3-pointer bounced off the rim at the buzzer.
The loss ended the Sky's six-game winning streak. Parker finished with 21 points and 11 reobunds.