The duo posted a new record total score with 195.52 points, made up of another record of 78.89 points for finishing first in the short programme on Sunday night and a season's best from the free dance routine, at the Iceberg Skating Palace in Sochi
It was enough to leapfrog Canadian rivals Tessa Virtue and Scott Moir, who pipped Davis and White to gold at Vancouver 2010.
With a tally of 190.99 they had to settle for silver in what was set to be their last competitive appearance while, to huge roars from the local fans, Russian couple Elena Ilinykh and Nikita Katsalapov came third with 183.48.
Reflecting on winning the USA's first ice dance gold medal, Davis said: "We're so excited, we're kind of in shock a little. I'm not sure what we're feeling.
"It kind of all came together for us and we're so pleased to be here. We're kind of in disbelief.
"I've never skated and visualised the performance at the same time and tonight that's kind of how it felt. It felt great."
White, on beating Virtue and Moir to first place, said: "The crowd was really alive out there today for all the teams and we fed off the energy.
"We were well prepared by our coach Marina (Zueva) in coming here and doing our job.
"I felt like we had done everything we could from the beginning of this competition, in practice, team event, this event.
"And 17 years of hard work was justified. To come away with a gold medal is amazing."
Asked how they handled the pressure of appearing in their last Winter Olympics, Virtue said: "This is the biggest stage in the world so, of course, it's stressful.
"It's a pretty ambitious programme and it's a loaded programme, and I think we did it pretty well. We felt immense pressure."
The Canadian duo bettered their previous season's best by more than two points, which gave Moir some consolation.
"It was what we wanted to do today," he said. "That was our best performance of the year for that programme.
"That programme was our baby and it's special for us to perform it for the last time."