Shea is a member of the first family with three generations of Olympians.
He dedicated victory to his grandfather, a former gold medal-winning speed skater, who died shortly before the Salt Lake City Games.
Galway-born aristocrat Clifton Wrottesley just missed out on claiming Ireland's first winter medal, finishing in fourth.
"My grandpa was with me the whole way"
Jim Shea Jr
Shea edged out Austrian Martin Rettl, who came second, with Gregor Staehli of Switzerland winning bronze.
The delighted gold medallist pulled a funeral card for his grandfather Jack from his crash helmet after clinching victory and waved it at the jubilant home crowd.
"The Olympics mean more to me than a gold medal. Now that I have one, I can say that," he said.
Britain's Kristan Bromley had a disappointing first run, and finished 13th.
The event, which had been considered too dangerous, was returning to the Olympic arena for the first time in 54 years.
Shea finished the two runs at Utah Olympic Park in 1 minute, 41.96 seconds, just 0.05 secs ahead of defending world champion Rettl.
Staehli, the 1994 world champion who came out of retirement to compete in the Olympics, clocked 1:42.15.
He edged out Wrottesley, who was seeking a surprise first Winter Olympics medal for Ireland and had been third after the opening run.
The victory completed an emotional two months for Shea, whose 91-year-old grandfather, Jack Shea, died from injuries sustained in a car accident.
Jack Shea, who won two speed skating gold medals at the 1932 Lake Placid Games, was America's oldest living Winter Olympian.