The Dutchman became the first man to break the 13 minute barrier, setting a new standard of 12 minutes 58.92 seconds at the Utah Olympic Oval.
He finished more than 11 seconds ahead of his compatriot, and former record holder, Gianni Romme.
Norway's Lasse Saetre, skating in the last pair, came third in the 25-lap marathon, 18 seconds behind the winner.
It was the second time that Uytdehaage had set a world record in claiming gold at the Games.
And, as in his previous effort in the 5,000m, it was Romme's record and Olympic title he took.
Uytdehaage, who has enjoyed a meteoric rise up the rankings, gradually built up his speed as the landmark became a possibility.
"This was an almost perfect race," the 25-year-old said.
"With seven laps to go I felt good - but a little tired of course.
"But I knew I was going to break the world record when my coach was just yelling and yelling," he added.
Romme started at a fast pace and was within the required time but began to tire before finishing in a time of 13:10.03.