Gibson, from Prestwick and Fear, who train in Montreal, scored 74.26 in the rhythm dance at the competition in Graz, Austria, just short of their season's personal best.
Reigning champions Gabriella Papadakis and Guillaume Cizeron from France placed first after the rhythm dance, followed closely by Russia's Victoria Sinitsina and Nikita Katsalapov,. The French pair edged the lead by just 0.05 points, creating an exciting free skate on Friday.
Gibson told The Scotsman: "We're very happy with our skate and looking forward to the free dance tomorrow."
In yesterday's pairs competition, Britain's Zoe Jones and Christopher Boyadji placed 11th, qualifying for the free skate.
Sheffield's PJ Hallam did not qualify for the mens' free skate after the short programme on Wednesday.