Wolff - in just his third start as a professional - rolled in a 30-foot eagle putt on the closing par-five at TPC Twin Cities to edge out playing partner Collin Morikawa and Bryson Dechambeau by one shot.
Playing in the final group together, Wolff and Morikawa stood in the fairway at the 18th and watched Dechambeau roll in an eagle putt of his own to set the clubhouse lead at 20 under.
Showing little nerves, both Wolff and Morikawa - also a newly minted professional - safely carried the water to find the putting surface with Morikawa slightly closer to the hole than his rival.
Wolff was well known as an amateur for his highly unorthodox golf swing as well as his brilliant record and proved his mental strength beyond doubt by rattling his ball into the flag.
AMAZING! @Matthew_Wolff5 makes EAGLE to win!July 7, 2019
It forced Morikawa to make his putt to force a playoff but his effort missed narrowly to the low side of the hole.
Wolff is the youngest first-time winner on the PGA Tour since Jordan Spieth won the 2013 John Deere Classic as a 19-year-old.
Canadian Adam Hadwin finished alone in fourth at 18 under ahead of Carlos Ortiz and Wyndham Clark who shared fifth at 17 under.
The 3M Open was not a good week for the Australians with Rod Pampling leading the way in share of 56th.
Western Australian Curtis Luck shared 58th while Jason Day finished the week at 5 under to be equal 66th.
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