Gillings - fifth at the recent World Cup in Montafon - posted the seventh best time to make Saturday's knockouts, taking just one run to advance.
She will now line up against Canadian world silver medallist Dominique Maltais in her quarter-final. Maltais was the second best qualifier behind American Lindsey Jacobellis.
Fellow snowboarder Aimee Fuller defied terrible conditions at Copper Mountain to finish 11th in qualifying at the women's slopestyle World Cup.
She missed the top eight that advance to the final but importantly ticked off one of the all-important top 12 Olympic selection standard, while British team-mate Katie Ormerod ranked 31st.
Elsewhere, Anna Vincenti, skiing with a broken thumb, didn't make the top eight required to qualify for the women's ski slopestyle final while Sochi ski cross hopefuls Emily Sarsfield, Pam Thorburn, Ed Drake and Pete Whelan all failed to finish in the top 32 needed to make Saturday's knockout races at their event in Italy.
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