A television replay showed that Hanson struck his chip shot on No. 12 a second time. He fell two strokes behind with four to play before making birdies on the 15th and 17th at the 6,915-yard Pula Golf Club.
Hanson won his third European Tour title when Canizares bogeyed the first extra hole.
Hanson and Canizares both shot 66 to finish 6 under, four shots clear of South Africa's James Kingston.
Christian Cevaer of France and Gonzalo Fernandez-Castano of Spain tied for fourth at 1 under.
"It feels absolutely fantastic after all that happened," said Hanson, who was shown footage of his double hit after his round was complete.
"It looks strange, but of course it was a double hit," he said. "The ball went down and then I hit it again."
Hanson could return to the top 50 in the world ranking, and he would need to stay there for one more week to avoid U.S. Open qualifying. He qualified for the U.S. Open last year by making a hole-in-one in a playoff.
Canizares, the son of former Ryder Cup player Jose Maria, was bidding to win his second European Tour title. He now has three consecutive top-10 finishes.
"I played very well today. On Friday and Saturday, I was not there, but today I didn't miss many shots," he said.