Gibson, from Prestwick and partner Lilah Fear, skated to rapturous applause in the free dance - the final competition of the European Figure Skating Championships - equalled only by the audience's response to the local Belarusian and Russian teams. Their programme was one of the most popular among the packed crowds at Minsk Ice Arena in Belarus.
The pair scored 112.28 in the free dance, narrowly missing their season's best of 113.29, scored at the British Championships in December. Their combined score was 182.05, moving them up a place past former GB skater Olivia Smart and her partner Adrian Diaz, who represent Spain.
Gibson, 24, and Fear had placed seventh after the rhythm dance programme yesterday, saying they would be "delighted" with a top ten finish.
Meanwhile, silver Olympic medalists Gabriella Papadakis and Guillaume Cizeron from France took the gold medal for the fifth time, with a seasons's best score of 133.19 and an overall score of 217.98. Meanwhile, Russians Alexandra Stepanova and Ivan Bukin took the silver and Italy's Charlene Guignard and Marco Fabbri the bronze with overall scores of 206.4 and 199.84 respectively.
"That totally smashed the top ten aim out of the water," Gibson told The Scotsman. "We are so happy. We really felt the crowd was behind us."
"It still hasn't hit me properly yet," said Fear, 19, who teamed up with Gibson, a former singles skater, in July 2016. "It's just crazy."
Teammates Robynne Tweedale and Joseph Buckland, who also skate for Great Britain, placed 17th after a solid perfomance in the free dance. The pair were ranked 18th after the rhythm dance. Buckland, who is the younger brother of previous British champion Nicholas Buckland, who this year retired with partner Penny Coomes.
Gibson and Fear's success means that two British couples will again have the chance to compete in the European championships next year - a privilege only afforded to nations who have a competitor in a top ten position.
The pair said they would soon start to plan next season's programme, with Fear, a student at McGill university in Montreal, where they train with renowned coach Romain Haguenauer, saying that she first needed to concentrate on her homework. The World Figure Skating Championships in Japan in March will be the last competition of the season.
"I have assignments due in next week, then we'll start thinking about the music for next year," she said. "We will be sad to stop skating this programme, we've enjoyed it so much."
The couple made major changes to the beginning of their rhythm dance programme ahead of this week's championships, which paid off after judges yesterday awarded them a score of 69.77, beating their season's best by five points.
Their programme this year, to disco music by Donna Summers, has been well received by judges and audiences alike.
"Maybe disco again?" joked Gibson, who took up skating after watching Dancing on Ice on TV. "There's enough music to choose from.