Højgaard had been two shots behind the leader heading into the 17th hole, but sensationally chipped in for eagle from over a bunker to tie Winther.
His stay at the top of the leaderboard was short-lived, with Winther immediately responding on the 16th with an eagle of his own, putting out after landing his drive on the green of the 304-yard par four.
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The 38-year-old made par on the 17th and 18th to end his final round with a five-under-par 67, and took a two-shot clubhouse lead over China's Yanhan Zhou.
Zhou needed a hole-in-one on the par-three 18th hole to force a play-off with the Dane, but when he three-putted to make a bogey on the last, Winther's three-shot victory at his home event was officially confirmed.
Zhou would finish his week tied for second at 12 under par alongside a group of five other players that included Højgaard, England's Matthew Jordan, Finland's Oliver Lindell and Italian Filippo Celli.
Winther, who had worked as a greenskeeper 15 years ago, had never thought he would become a professional golfer, let alone become only the second winner of the Danish Golf Championship.
"[It's] impossible to rank this," the 38-year-old said after his round. "Just after my kids' birth. It was amazing.
"I don't think it's sunk in yet. I'm overly happy; we've been clapped off on every single green. Even when we hit poor shots. Still getting clapped off! The crowds carried me all week. It's been unbelievable."
"I was never going to be a golfer. This is just insane, I'm in shock," he added.
More to follow...
Watch all four rounds of the DP World Tour's Nexo Championship, live on Sky Sports. First round coverage begins on Thursday at 12.30pm on Sky Sports Golf.
