The 28-year-old Zhao left three-time world champion Williams playing catch-up after he made a blistering start to take the first session 7-1 at the Crucible Theatre.
But the 50-year-old Williams, bidding to become snooker’s oldest world champion, fought back in the evening session.
That still left him five frames behind in the best-of-35-frame contest.
Williams is attempting to surpass Ronnie O’Sullivan, who was 46 years and 148 days old when he won his modern-day record-equalling seventh title in 2022.
The Welshman has reached the final despite his age and eyesight problems.
Zhao, playing as an amateur as he continues his comeback after a 20-month ban for involvement in a betting scandal, came through four rounds of qualifying.
He also produced a stunning display to thrash O’Sullivan 17-7 with a session to spare in his semi-final.
On Sunday, Zhao, the 2021 UK Championship winner, started in commanding style by taking each of the first three frames, including two century breaks.
Williams reduced fellow left-hander Zhao’s lead to 3-1.
Following the mid-session interval, Zhao, only the second player from China to reach the world final after Ding Junhui, restored his three-frame advantage with a break of 57.
Williams found some form with a break of 61, only to misjudge a cannon off a black with the frame at his mercy. He was then unable to make a fine cut on the red and Zhao cleaned up.
Zhao wrapped up the first session in style, making a break of 104 before a superb plant on a red led to a contribution of 83 that put him six frames ahead.
Williams won Sunday evening’s opening two frames.
But Zhao, in his first world final, regained control with a break of 71 to go 8-3 up before taking the next to restore his six-frame lead.
Williams went 23-0 ahead in the 15th frame only to let Zhao back in with a couple of missed reds.
Zhao then produced a superb positional pot, as he went around the angles from red to blue, that sparked an impressive break of 96 and a 10-5 lead.
Williams was on the brink of winning the next frame with a break of 63 only to miss a clinching red. Zhao then held his nerve superbly with a clearance of 71 to restore his six-frame advantage at 11-5.
Sunday’s final frame proved a nervy affair before Williams, benefiting from a fortunate snooker behind the green, reduced his arrears to five frames.
The final resumes at 1200 GMT on Monday. (AFP)
