Nina had scored just 18 points out of 40 for her Tango on Saturday and was voted off after head judge Shirley Ballas was given the casting vote.
Shirley said: “Well this is one of the closest battles I think we’ve ever had in a dance off. Both couples upped their game. Both couples were absolutely delightful to watch. Neither couple had mistakes so I’ve decided to go with the couple who had more advanced technical actions in their dance and that couple is Katie and Gorka.”
When asked by Tess about their time on the show, Nina said: “It’s been really fun, thank you so much. [Neil] is incredible, thank you.”
Neil was then asked if he had any words for his partner, adding: “You’ve been a dream. Second partner on the show for me. I wouldn’t have wanted anybody else. You’ve been fantastic and so much fun. Literally, we’re like a married couple - you’ve got both husbands here tonight!
“It’s been so much fun together, you said you wanted to dance and you’ve done two fantastic dances and I’m really, really, really proud of you.”
AJ Odudu and her partner Kai Widdrington topped the overall leaderboard for the first two weeks.
Next week the remaining 14 couples will perform in this year’s Movie Week special.
Strictly Come Dancing continues on BBC One on Saturday at 6.45pm.