Casey started the day four shots behind overnight leader Romain Wattel but the Englishman carded a four-under-par 66 at the Kennemer Golf Club in Zandvoort to finish in a total of 266.
Three-time tournament winner Dyson finished one shot off the lead after making a late surge up the standings thanks to a five-under-par final round of 65 that piled the pressure on Casey.
The 37-year-old Casey, who shot a course-equalling 62 on Saturday, stood strong to claim his first European Tour title since last year's Irish Open.
Englishman Andy Sullivan, who finished third two shots behind Casey, had reason to celebrate when he made a hole-in-one on the 15th to win a trip into space from sponsor XCOR Space Expeditions valued at $95,000.
(Reporting By Michael Hann, editing by Alan Baldwin)
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