The 40-year-old Karl tore off his shirt to celebrate bare-chested on the snow-covered slopes of Livigno in the Italian Alps, pumping his arms and shouting.
Karl, who has said he plans to retire after this season, edged silver medallist Sangkyum Kim of Korea by 0.19 seconds.
The triumph handed him his fourth Olympic medal. He earned silver in Vancouver in 2010, a bronze at Sochi in 2014 and gold at Beijing in 2022.
Tervel Zamfirov of Bulgaria earned bronze in a photo finish over Slovenia's Tim Mastnak, the silver medallist in Beijing.