Webb Simpson finished alone in third position albeit four shots behind McNeil.
In his very first start in the event, Cabrera adds this title to the 2007 US Open and 2009 Masters titles, not to mention his near miss at the 2013 Masters where he lost a playoff to Adam Scott.
Early in his final round McNeil had given little evidence of what was to follow but four birdies and an eagle from the fourth hole set the tone for his round and when he added three further birdies through his back nine he set the target for Cabrera who had only just made the turn when McNeil finished.
McNeil's eagle came courtesy of a hole in one at the 8th hole, adding further to a day of highlights on the low scoring layout.
Cabrera though would also reel off a run of birdies and an eagle of his own when birdied the 11th and 12th then holed a 7 iron from 175 yards for an eagle at the 13th to move to 17 under and three clear.
No sooner had he established an apparently unassailable margin than Cabrera dropped consecutive shots at the 14th and 15th and the margin was just one.
Cabrera though was driving the ball beautifully and after a magnificent tee shot at the 17th he found the green at the par five and two putted for a birdie to open the gap to two.
Only the par three 18th remained and although he had played the hole in a total of three over in his first few rounds he safely found the green when it counted and two putted for his impressive win.
Cabrera had begun to play well in recent weeks after what had been a very slow start to the year and with the Open Championship just ten days away then he is peaking at the right time. Cabrera does not enjoy a great record at the Open Championship with just two top tens in 15 starts but he is an unpredictable golfer at times and might just do well at Royal Liverpool.
The leading Australasian this week was New Zealander Danny Lee who was 16th while Robert Allenby led the Australians in 27th position after missing his last four cuts in succession.
Tim Wilkinson and Bronson La'Cassie finished 57th and Oliver Goss 68th.
The PGA Tour now heads north to Illinois for this week's John Deere Classic.