The tourists lead by 381 runs with seven second-innings wickets remaining after bowling out their opponents for 188 at Senwes Park.
The usually fluent Hales, likely to open alongside Alastair Cook in the first test against South Africa starting in Durban on Dec. 26, repeated his first-innings score when he was bowled on eight, again falling to seamer Junior Dala after having laboured for 42 balls.
Cook (37) looked in fine touch before he was trapped leg before wicket, also for the second time in the game, while Nick Compton (15) could not repeat his first-innings half-century. Joe Root (25 not out) and Gary Balance (six not out) will resume on the final morning on Thursday.
Stuart Broad had earlier impressed with the ball in recording figures of three for 18 as the inexperienced home batting line-up were dismissed for 188.
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That included a 51-run last-wicket stand, the only frustration for the bowling attack on the day.
Seamer Mark Footitt was expensive but bagged figures of two for 51 from 12 overs, while all-rounder Ben Stokes followed up his century with the bat on Tuesday with figures of two for 25.
Each side may use 13 players in the game, which does not carry first-class status, and can bat for a maximum of 100 overs.
The first test will be followed by matches in Cape Town, Johannesburg and Pretoria.
(Reporting by Nick Said; editing by Clare Fallon)
