Kalla – the 34th cross-country skier out of the gates in Germany – looked like taking the first stage victory of 2012-13 Tour de Ski amid heavy mist.
She completed the prologue in 7:32.5minutes to lead right up until Randall crossed the finishing line having been among the last three to start.
Randall went 4.4seconds quicker than Kalla, who won Olympic gold in the 10km freestyle at Vancouver 2010, to take the early lead in the Tour de Ski.
There was disappointment as the Tour de Ski began with Marit Bjoergen absent after experiencing an irregular heartbeat but joy at the end for Randall.
She claimed her first stage win in the Tour de Ski in Oberhof and also beat the winner of the last three overall titles Justyna Kowalczyk.
Kowalczyk won this stage 12 months ago ahead of Bjoergen but was down on Kalla, let alone Randall, early on finishing 4.7seconds behind overall in third.
And American Randall is determined to hold onto the leader’s jersey after the second stage, a 9km classic pursuit, on Sunday.
“It feels really hard but it is a big accomplishment and I am pretty happy with the stage victory,” said Randall.
“There is an unbelievable excitement being in this position, it is fun. I know there is a big target on me now.
“But I will try and hang in there in the classic and have anther strong race.”