Randall clinched the 3.1-kilometre sprint by leaving Charlotte Kalla of Sweden 4.4 seconds behind. World Cup leader Justyna Kowalczyk of Poland was third, 4.7 seconds back.
The tour consists of seven events over nine days in Germany, Switzerland and Italy.
Randall finished last season's series in 10th place and was second in the sprint prologue.
Petter Northug of Norway won the men's 4-kilometre prologue to stretch his World Cup lead. Northug beat Marcus Hellner of Sweden by 6.1 seconds, while Alexander Legkov of Russia was 7.2 seconds behind.
Three-time tour winner Dario Cologna of Switzerland was 10.1 seconds back in fourth while Alex Harvey of St-Ferreol-les-Neiges, Que., was the top Canadian in sixth place.
Ivan Babikov of Canmore, Alta., was 32nd, Devon Kershaw of Sudbury, Ont., was 48th and Toronto's Len Valjas was 52nd.