South Australia put up bold resistance Friday as they chased a daunting target of 446 runs for victory off 153 overs but Bichel claimed five wickets to finish with nine for the match.
The home side made 392, after losing five wickets for 254 on the last day.
Queensland were frustrated by three productive partnerships, particularly a ninth-wicket stand of 67 by Daniel Cullen (19) and Shaun Tait, who thrashed four sixes and three fours in making 58 off 57 balls -- his first half-century in 15 Shield matches.
Bichel broke the ninth-wicket liaison by having Cullen caught at forward short-leg and he then had Tait caught in the gully -- for innings figures of 5-73 and a grand Man of the Match return of 9-144 off 41.1 overs.
Earlier, Callum Ferguson fell just seven runs short of his maiden first-class century in only his second match.
Ferguson and Graham Manou shared an aggressive sixth-wicket partnership of 127 in 28 overs, including 91 off 17 overs today, until Manou, SA's captain, was caught behind for 81 off just 88 balls.