Scheffler, who closed with a 63 to finish at 31 under par with a four-round total of 253, tied the mark set by Justin Thomas at the 2017 Sony Open and equalled six years later by Ludvig Aberg at the RSM Classic.
The world's top-ranked player was in position to break the record before a flubbed chip that led to bogey on the par-3 17th hole and a par from a greenside bunker on the par-5 closing hole. His eight-foot putt for birdie and the record slid by the left side of the hole.
Hideki Matsuyama has the lowest score in relation to par this season, 35 under on the par-73 Plantation Course at Kapalua.
Scheffler tied the 54-hole Nelson record with an eight-shot lead, and nobody got closer than six during the final round.
South African Erik van Rooyen matched Scheffler's 63 to finish at 23 under, three shots ahead of Sam Stevens and four ahead of another home-town favourite, Jordan Spieth.
Spieth and Scheffler finished with the two lowest rounds of the tournament.
Scheffler opened with a 10-under 61 on Thursday at the defenceless par-71 TPC Craig Ranch in a suburban community about 50km north of Dallas.
Spieth shot 62 in the final round, surging to finish fourth while watching his friend and fellow Texas alum become the first of the pair to win the event they both cherish.
It was the first victory this year for Scheffler after he won a total of 10 times before May in the previous three years combined, including two Masters victories.
The 28-year-old Dallas resident has 14 career victories.
Scheffler's previous best Nelson finish was a tie for fifth two years ago.
He missed last year's event for the birth of his first child.
Scheffler cradled his year-old son, Bennett, after becoming the first wire-to-wire Nelson winner since Tom Watson 45 years ago.
The American shattered the previous Nelson scoring record of 259 set by Australian Steven Bowditch in 2015.
That tournament was played at the TPC Four Seasons. Normally a par 70, that course had a par-69 layout the final three days when heavy rain forced officials to convert a par-4 into a par-3. Bowditch finished 18 under.
Scheffler's victory margin was the second-largest at the Nelson behind Sam Snead's 10-shot win in 1957, when it was known as the Dallas Open Invitational.
Because of heavy rain on Wednesday and Friday, players were allowed to lift, clean and replace their golf balls in the fairway for the first three rounds, but not in the final round.
Karl Vilips was the leading Australian, finishing at eight under in a tie for 49th place after rounds of 65, 72, 69 and 70.
Fellow Aussie Cam Davis tied for 60th at five under the card.
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