Mark Footitt took his first wicket for England as the tourists continued to dominate on day two of their warm-up against a South African Invitational XI in Potchefstroom.
Having declared on their overnight total of 470 for five, built around centuries from James Taylor and Ben Stokes, England then made regular breakthroughs in the morning session to leave the hosts 86 for five at lunch.
Stuart Broad struck twice in his opening spell, having Aiden Markram caught at first slip by Alastair Cook with the fourth ball of the day.
Luthando Mnyanda then played on for seven, before left-arm seamer Footitt - who has joined Surrey from Derbyshire over the winter - had Zubayr Hamza caught behind for 12 to leave the Invitational XI 43 for five.
Opener Simon Khomari made 20 before being caught by Taylor off Chris Woakes, and Stokes' excellent return to action from a shoulder injury continued when Bairstow caught Somila Seyibokwe down the leg-side for one.
From 56 for five, Qaasim Adams and Heinrich Klaasen showed some resistance with an unbroken 30-run stand for the sixth wicket, but the home side were still 384 runs in arrears at the break