The 27-year-old birdied the second extra hole to edge out England’s Joe Dean and Sweden’s Marcus Kinhult after the trio had all finished tied on 11-under-par on Sunday.
All three birdied the first extra hole, the par-5 18th, but Migliozzi was the only one able to repeat the feat after finding the green in two and two-putting from long range.
Kinhult’s chances effectively disappeared when he hit his second shot into the water surrounding the green, while Dean missed from 20 feet for birdie after a wayward drive meant he could not go for the green in two.
Former delivery driver Dean had the consolation of joining Migliozzi in securing the two qualifying places for next month’s Open Championship at Royal Troon, Dean’s higher world-ranking giving him the berth ahead of Kinhult.
Migliozzi had earlier carded four bogeys in six holes from the 9th, but birdied the 16th and 18th to complete a final round of 70 and get into the playoff, with Dean also making a birdie on the last, in a back nine of 30, to catch Kinhult.
“It’s been a great battle,” said Migliozzi, whose bogey on the 10th came after he could not find his original drive inside the permitted three minutes.
“After I lost the ball on 10, inside me I was like ‘If I can go through this, then I can do it’. I never thought I was done. I always try to make birdies and come back and here it is now. It’s an incredible feeling.
“It’s super, super nice to be here now.”
Finland’s Mikko Korhonen, who took a one-shot lead over Migliozzi into the final round, struggled to a closing 75 to finish in a tie for 10th.
Denmark’s Rasmus Hojgaard and Italy’s Andrea Pavan finished a shot outside the play-off, Pavan having set the early clubhouse target following a superb 65.
Tee times had been delayed by two hours on Sunday when Extinction Rebellion activists blocked the entrance to The International course.
The first eight groups had already teed off but the remaining ones were pushed back, with the leaders eventually getting under way at 3pm local time.
Australians Andrew Martin, who finished with a 73, and Thomas Power Horan (70) both ended up on one-over for the tournament, among a group who were tied for 51st place.
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