The early games of the first set went with serve but after Zheng held serve to lead 5-3, Williams was broken, losing the first 6-3 in 40 minutes.
The American came out fighting in the second, getting an early break in the first game. Williams was soon 4-1 to the good after another break.
She subsequently served out for the set 6-2.
The third set was a hard-fought affair, although Zheng did secure an early break. With a 4-1 advantage, the Chinese player appeared to be in control, but Williams fought back and broke.
Both were breaking each other's serve with regularity, and after one more break each, the set went to a tie-break.
Zheng found herself 4-1 down, but recovered to win the set and match.