Man of the Match Bichel backed up from his 10-wicket match haul to edge his way to 28 from 47 balls to get Queensland home after a rain-hit final day's play on Monday.
The win gave Queensland a maximum six competition points with 22 balls to spare in the twilight.
Bichel had come to the crease with the floodlights on and NSW on a roll as Queensland, chasing 240 for victory, had slumped to 182 for six.
With Nathan Bracken (5-49) and Matthew Nicholson (2-54) proving difficult to play in the bad light, the 34-year-old gained superb support from Martin Love (six) and Ashley Noffke (15 not out).
South Australia shared the honours with the Shield champions Victoria to set up a final day showdown at the Adelaide Oval on Tuesday.
After losing their way in the middle order, the home side finished their second innings with a flourish to set the Victorians 321 to win.
They declared at 289 for six just before the close of the third day and grabbed the wicket of opener Matthew Elliott for two to be 7 for one at the close.
Former Test opener Greg Blewett top scored for South Australia with 89 while rising star Mark Cosgrove hit 57, including 11 boundaries to follow his 82 in the first innings.