Green had an opportunity to force a playoff with Dyson at minus-15 if he could par No. 18. His 65-foot birdie putt try came close, but it then continued 12 feet past the hole.
Needing the second putt to force sudden death, Green missed, and Dyson earned his fifth European Tour victory and first in almost two years.
Dyson carded a 4-under 67 Sunday to finish at 269, while Green shot a 3-under 68, ending one back at minus-14.
Stephen Gallacher (68) claimed sole possession of third, finishing two behind the leader at 12-under 272, while Bernd Wiesberger fired a 5-under 66 to grab fourth at minus-11.