Dyson fired a 7-under-par 63 in the final round to reach the playoff with Peter Lawrie (67) and Peter Hedblom (69).
The three had completed regulation play at 15-under-par 265.
Dyson, 31, has three wins on the European Tour. His other KLM victory came in 2006.
"Unbelievable," Dyson said after his latest win.
Dyson, who had only two bogeys in the tournament, said he played the best golf of his career.
"Every part of my game -- my driving was good, my iron play was good and when I did miss the green my chipping was good," Dyson said. "And when I did not hit a very good chip, I made the putt."
Damien McGrane (64) was fourth at 266 and Jamie Donaldson (67) and Darren Clarke (68) shared fifth at 267.