Humphries, who won Olympic gold at Vancouver 2010, headed into the ninth and final round in Russia, also acting at the test event for next year's Games, with a 187-point lead over Kiriasis at the top of the standings.
With 225 points on offer for the win it would have taken a miracle for Kiriasis to overthrow the Canadian in Sochi and so it proved with Humphries' third place enough to wrap up the World Cup title.
Kiriasis took victory for the second successive race having won in Igls last time out to maintain her overall standing of second while Elana Meyers did enough for third in the Russian Olympic host city.
Humphries' World Cup triumph ends a run of 11 straight German victories, eight of which have come from Kiriasis while she is also the first Canadian to achieve such a feat.
It was Kiriasis who set the early pace in Sochi as she clocked 58.16seconds for the lead after the first run with compatriot and defending champion Cathleen Martini in second with 58.20 and Humphries third with 58.24.
Meyers was fourth after posting 58.33 before producing the quickest time of the second run, 58.99, to jump up into second overall just 0.13 behind Kiriasis, who was second fastest for the win.
Humphries again went third quickest to remain in the same place overall and with it secure her first World Cup title to go with the Olympic gold she won in 2010 and the World Championship title she retained two weeks ago.
Martini slipped to fourth overall after posting the seventh fastest time while British No.1 Paula Walker finished down in 16th for her worst finish of the season at the ninth and final round.
She once again had company in fellow British pilot Victoria Olaoye, who ranked 19th after the two runs at the Olympic venue 2.56 behind winner Kiriasis.