Zhu then won four games in a row to take a set two lead of 4-2.
Play resumed on an indoor court after a second rain delay with Zhu holding serve then breaking serve to level the match 6-3, 2-6.
On set point, Zhu struck a crosscourt backhand winner to end the set.
In the final set, Williams looked to have the match under control as she took leads of 4-2 and 5-3.
Serving to stay in the set, Zhu took a 40-15 lead before Williams struck a down the line forehand return long to lose the game.
Serving for the match at 5-4, Williams netted a crosscourt backhand before committing two crosscourt forehand errors to trail 15-40.
Williams netted an additional crosscourt backhand to drop serve and level the set at five all.
Zhu held serve in the following game to lead 6-5 following several additional errors from Williams.
Serving to stay in the set at 15-30, Williams struck a powerful crosscourt backhand to reach 30 all.
However Williams then hit a down the line backhand long to trail 30-40 and face matchpoint.
Williams netted a sitter down the line forehand to end the match.
Williams' unforced errors for the day totaled 38 to 30 winners in the two hour 23 minutes long match.
Williams will look to even out her game which appeared up and down in Auckland before the Australian Open which begins January 15th in Melbourne.