Trailing third-round leader Joost Luiten by four shots starting the final day, Casey grabbed control with a stretch of five birdies over six holes from No. 8, then drained a 50-foot putt on the last to punctuate the win, ending at 14-under-par 274.
The four-shot turnaround tied him for the biggest comeback in event history and handed the British golfer his 12th career European Tour triumph.
Luiten, meanwhile, stumbled to a 2-over 74 at Carton House Golf Club, ending alongside Robert Rock (71) in second place at minus-11.
Sole possession of fourth place at 9-under 279 went to Pablo Larrazabal (75).