The Six Nations champions are underdogs for the last-four showdown in Yokohama City, where they will be striving to reach the final for the first time.
Wales left it late to beat 14-man France at the quarter-final stage last weekend and must do without full-back Liam Williams (ankle) and flanker Josh Navidi (hamstring) against the Springboks.
Centre Jonathan Davies has been passed fit after a knee problem, though, and head coach Gatland is optimistic his side can defy the odds to earn a shot at the Webb Ellis Cup.
