After being reduced to 3-141 at lunch on Saturday, following Bashir's breakthrough for England in the first session, the touring side immediately lost batter Ben Curran when play resumed.
Bashir struck with his second ball to dismiss Curran, who found Ben Stokes at short extra cover, falling for 37 off 104 balls.
Just when all-rounder Wesley Madhevere tried to stabilise the innings for Zimbabwe (31 runs off 36 balls), Harry Brook pulled off a stunning one-handed catch mid-air at slip off Stokes' bowling, leaving his captain stunned by the brilliance.
From then on, wickets kept tumbling for Zimbabwe as Tafadzwa Tsiga (4) and Blessing Muzarabani (0) were removed cheaply while Bashir continued to wreak havoc with the ball.
Bashir claimed his fifth wicket by dismissing all-rounder Sikandar Raza, who scored 60 runs off 68 balls.
The 21-year-old then took his sixth wicket, removing Tanaka Chivanga who was trapped leg before.
Earlier, Sean Williams had given Zimbabwe a fighting chance, scoring 88 off 82 deliveries, before the former Zimbabwe skipper was sent packing by Bashir.
Williams, who scored his sixth Test half-century, was trapped lbw by Bashir.
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