Needing just a par five at the last to secure victory in regulation play, the American uncharacteristically took three from the edge of the green.
That meant extra holes with South African Grace, who was already in the clubhouse on 17 under at that stage.
But on the first trip back down the 18th, Mickelson produced a stunning wedge to within a few inches of the cup and Grace could not match his birdie.
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Aberdeen Standard Investments Scottish Open takes place at Gullane Golf Club in East Lothian, Scotland and forms part of the European Tour’s Rolex Series. The 2017 defending champion is Rafael Cabrera-Bello and will be joined again this year by Rickie Fowler, Phil Mickelson, Patrick Reed and Justin Rose.
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