Goals from Ferjani Sassi, skipper Youssef Msakni and substitute Naim Sliti secured a 3-0 quarter-final win in Cairo to set up a showdown with Senegal on Sunday, but it was Khazri who led the way with a fine individual display.
Tunisia enjoyed the better of a keenly-contested first half, but were unable to make the pressure count.
St-Etienne's Khazri came closest to breaking the deadlock with a curling 32nd-minute free-kick which Melvin Adrien clawed away, and the Malagasy keeper had to get down well to turn away Ghaylen Chaaleli's well-struck effort 10 minutes later.
Khazri thought he had broken the deadlock seconds after the restart after sliding the ball past Adrien, although a late, but correct offside flag ended his celebrations.
However, the opening goal did arrive with 52 minutes gone when Sassi's shot took a wicked deflection off defender Thomas Fontaine and wrong-footed the keeper.
It was 2-0 on the hour when Adrien could only parry Khazri's effort and Msakni followed up to find the bottom corner, and the former Sunderland midfielder fed Sliti to complete the scoring in stoppage time.