After six birdies in his first 12 holes, Dyson matched a course record with a 7-under 63 and then birdied the first extra hole for his second title at the KLM Open.
Dyson previously won in 2006 on another 18-foot birdie putt.
When I birdied the seventh and ninth I thought back to doing the same when I won, Dyson said. Then I birdied the 12th like I did then.
Lawrie was one ahead of Dyson with three to play until he bogeyed the 16th, while Hedblom lost his fourth career playoff by missing a 25-foot putt.
Defending champion Darren Clarke settled for fifth alongside Welshman Jamie Donaldson.