Jansrud, a bronze medallist in the downhill a week ago, posted a time of one minute 18.14 seconds to leap to the top of the standings at Rosa Khutor Alpine Centre.
His time was 0.3secs quicker than nearest challenger Andrew Weibrecht, with his fellow American Miller and Canadian Jan Hudec sharing bronze with an identical time of 1:18.67.
Sweden saw off stiff competition from Russia and France to take gold in the men’s 4x10km cross-country relay.
An impressive final run from Sweden’s Marcus Hellner secured gold for his team, with Russia and France making up the podium.
The men’s biathlon 15km mass start fell victim to fog last night, making the event the first to be called off at the Sochi Games.
Eva Samkova of the Czech Republic clinched the gold medal in the women’s snowboard cross as American favourite Lindsey Jacobellis crashed out once again.
Jacobellis, who famously blew gold in Turin in 2006 when she fell attempting a stunt on her final jump, slid out of contention after falling when well ahead in her semi-final.
Samkova executed a clear run to ease to victory ahead of World Cup leader Dominique Maltais of Canada, with French teenager Chloe Trespeuch taking bronze.
Jorienter Mors broke a 12-year-old Olympic record to grab gold in the 1500 metres speed skating final.
The 24-year-old Dutchwoman blitzed the field in a time of 1:53.51 seconds. She beat defending champion Ireen Wust into second. Lotte van Beek made it a clean sweep of medals for Holland.
The first two runs of the two-man bobsleigh saw Russia 1 leading the way on a combined time of 1:52.82.
That put them 0.32secs ahead of Switzerland 1, while the United States’ first crew lay in third.
It was Jamaica who won the popularity contests, however, delighting the crowd despite coming in bottom of the 30-team pile.
The ice dance figure skating competition also began last night, with USA pair Meryl Davis and Charlie White leading the way following the short programme.