The visiting skipper struck 116 (188 balls, 15 fours, 1 six) to rescue his team from early trouble to eventually post 268 all out after five wickets from spinner George Linde.
The slow-left armer bagged 5/55 in 20 impressive overs, while there were also three wickets from Lizaad Williams (3/51).
Gqadushe shared in a vital 135-run fourth wicket stand with Kyle Nipper (69) after the KZN side had slipped to 21/3. Gareth Dukes also aided his skipper to put on 44 for the seventh wicket as the visitors were all out in 80.4 overs.
In reply, WP reached 58/2 with a wicket apiece for Dukes (1/11) and Graham Hume (1/17).