The Blues secured victory in the second session of the final day's play, with wrist-spinner Casson, the pick of the NSW bowlers (4/126), plucking up the last wicket to fall before being swamped by delirious team-mates.
Stuart Clark (2/29), Stuart MacGill (2/118) and Brett Lee (1/68) all offering solid support.
This is NSW's 45th interstate title win in the Cup (earlier Sheffield Shield) history.
The Bushrangers resuming the fifth day at 2/96 lost four wickets in the first session to end any remote hope of drawing the tie.
David Hussey (33), Cameron White (57), Andrew McDonald (4) and Nick Jewell (99) all departed before lunch and then it was just a matter of time before the Blues began celebrations.
The visitors' four remaining wickets fell between lunch and tea with the unlikely victory target still a distant 259 runs away.
Hussey failed to add to his overnight score, driving Lee to Casson in the covers in the first over of the day.
White and Jewell put together an entertaining 115-run partnership before the skipper was out shortly before the interval.
Attempting to drive Clark down the ground, White got a leading edge and Nathan Bracken at mid-on held on to a high catch. White struck seven fours and two sixes in a free-flowing 72-ball knock.
McDonald lasted just 10 balls before he was caught by Simon Katich at bat pad with the score on 222.
Jewell was cruelly denied a century, given out lbw to Clark on the last ball before lunch.
Peter Siddle (18) and Crosthwaite took up the challenge in the second session and put together a useful 40-run partnership before it was broken in unlucky circumstances.
Crosthwaite belted a straight drive which deflected off Casson's hands and onto the stumps with Siddle, who was backing up, out of his ground.
Crosthwaite made 50 before he was bowled by a delivery from Casson which kept low.
Bryce McGain (25) reached his highest first-class score before being caught in close by Phil Jaques off Casson's bowling.
Tailenders Shane Harwood and Dirk Nannes then frustrated NSW in a 50-run 10th wicket partnership lasting half an hour. Casson finally triggered the start of Blues' celebrations, removing the obstinate Nannes (30) just before the scheduled tea break.
Shane Harwood remained not out 15. Blues' skipper Simon Katich was named man-of-the-match with 86 and 92.
NSW Blues 281&563/8 decl beat Victoria Bushrangers 216 and 370 (Jewell 99, Cameron White 57, Crosthwaite 50, David Hussey 31, Nannes 30; Casson 4 for 126, Stuart Clark 2 for 29, MacGill 2 for 118).