Hansen was sixth in qualifying over the flying 200m time trial and then produced two excellent wins in the opening two rounds of elimination competition and move into the quarterfinals.
It is already her best international performance to push into the top eight sprinters in the world.
World team sprint gold medallist Sam Webster finished seventh in the men's sprint competition.
He lost out to triple Olympic gold medallist and double world champion Jason Kenny, of Britain, 2-0 in the quarterfinals.
Hansen (26) qualified sixth-fastest in 10.949sec for the flying lap on a sluggish track to be only 0.2sec behind top qualifier Stephanie Morton, of Australia. It was a fraction outside the national record she set in Cambridge last month.
She beat German double junior world champion Emma Hinze in the first round, and came over the top of former Olympic speed skating medallist Laurine van Riesse, of the Netherlands, in the second round.
Webster also secured a top-eight world ranking, finishing seventh in the men's sprint competition.
He found Kenny in outstanding form in front of a packed home crowd, with the British rider winning in two straight rides in the quarterfinals, before going on to claim the world title over Australian Matthew Glaetzer.
Webster finished third in the ride-off for fifth to eighth behind winner Fabian Puerta Zapata, of Colombia, a world championship medallist, and Frenchman Gregory Bauge, a nine-time world champion.
In other action, Aaron Gate was 17th in the 1000m time trial, 16th in the flying lap and 19th in the points race to finish 19th overall in the men's six-discipline omnium competition.
Lauren Ellis was 20th in the scratch race, eighth in the individual pursuit and 14th in the elimination race to be 15th overall after the first day of the women's omnium.
The New Zealand women's team pursuit quartet finished a heartbreaking fourth after missing out to host nation Great Britain in their bronze medal ride-off on Saturday.
Dylan Kennett finished seventh in the individual pursuit in 4min 19.992sec.
Young Manawatu rider Luke Mudgway failed to finish in the points race. He pushed himself up to sixth but faded in the hard-fought 40km event.
