The 27-year-old Chinese player raced into a commanding 3-0 lead, capitalising on a sluggish start from the two-time champion.
World number nine Selby momentarily found his rhythm, pulling one back with a superb 71 clearance in frame four, but he never truly recovered the momentum.
Zhou - ranked 37th in the world - held his nerve to close out victory and reach his fourth ranking event final.
The result marks a timely resurgence for Zhou, who had not advanced beyond the last 16 of any ranking tournament this year.
His last appearance in a final came at the 2022 Northern Ireland Open, where he was beaten by Allen.
Reflecting on his progress, Zhou said: "In this sport you need to be very strong mentally. When you are in the chair after missing a ball you need positive thoughts.
"This is a very big change for me this season. If I win the final, I will be very proud of myself. The first time, going from zero to one, is tough. It is not easy, but I will give my best and hopefully I can do it."
Allen sneaks past Jones
Allen had earlier secured his place in Sunday's showpiece after edging past Jak Jones in a dramatic deciding frame.
The semi-final was a high-quality affair, with both players compiling century breaks inside the opening five frames.
Jones, backed up by four additional half-centuries, built a 5-3 advantage and looked poised to upset the Northern Irishman.
But Allen dug deep, reeling off the final three frames with contributions of 79, 68 and 86 to reach his maiden English Open final.