The world number one dispatched of her Chinese opponent 6-0 6-1 as she played under the floodlights of Arthur Ashe Stadium for the first time in her career.
"I think you guys inspired me to play my best tennis," she said after the match. "It's an incredible atmosphere and energy.
"I always wanted to play here, I've watched on TV but it felt really different. It was amazing."
Azarenka will next take on Georgia's Anna Tatishvili for a place in the quarter-finals.