Randall was chasing her fourth victory of the season, and her second this year since opening up 2013 with a New Year's Day win.
But heading into the final it looked like Norway's Astrid Uhrenholdt Jacobsen was the woman to beat as she was the fastest qualifier.
However, Jacobsen ran out of steam as she finished just off the podium in fourth, while Randall stormed to the win in 2:44.03 minutes.
And after battling illness prior to the event, Randall was over the moon to adjust to the 2014 Olympic venue so quickly.
"It feels great to have the win and also get a taste of next year," said Randall, who saw France's Jean Aurore and Norway's Celine Brun-Lie finish second and third respectively.
"When you are ill all you want to do is ski but you can't, you just have to rest up. But thankfully I got to ski and I am really happy with the win and I can't wait for next year and the Olympics now."
In the men's event Norwegian Petter Northug held off the challenge of Switzerland's Dario Cologna to also pick up his fourth World Cup victory of the season.
The pair were locked into a battle heading into the final few metres but Northug had enough left in the tank to cross first, 0.57 seconds ahead of Cologna, with Italian David Hofer taking third.
Despite finishing second-best in Sochi Cologna still sits pretty atop the overall World Cup standings on 898 points, with Alexander Legkov second on 865 and Northug third on 859.