While Tilly had finished in joint second-bottom position on Saturday night’s leaderboard alongside Dan Walker with 29 points for her Quickstep, Sara had fared better with the judges, picking up 32 out of 40 for her Argentine Tango.
Craig said it was a “really difficult decision” because he gave both couples a seven on Saturday night.
“So very, very equal which made the decision even more difficult,” he said.
Motsi also said: “I have to say there were three factors that decided it for me; there were details, the nerves and a very strong competitor so I am saving Tilly and Nikita.”
While there was already a majority vote to save Tilly and Nikita, head judge Shirley Ballas agreed she would have also voted to keep them in the competition over Sara and Aljaz.
Following the result, Sara told host Tess Daly: “I had no idea any of this was in me. It’s been a life changing experience and one I’ve loved every second of.”
Aljaz said: ’I feel like from that day we met under the Angel of the North, I was so pleased to dance with you this season. Honestly, I wouldn’t want to dance with anybody else.
“You have been an absolute joy and a testament to hard work – not just on Strictly but with your business and you’re a beautiful mother. Thank you for letting me spend so much time not just with you, but with the whole family, the Davies’s that are here tonight, all of the little ones at home.
“I’ve been so welcomed up North, it made me feel like I’m back home in Slovenia because everyone is so lovely and friendly. I’m going to miss you so much. I’m going to miss dancing with you. I’m going to miss everything about this show. Thank you everyone and thank you for supporting us.”
Sara responded: “Aljaz is one in a million. I tell him every day and this wouldn’t have been the experience it was, if it wasn’t for him.”
After the show, the presenter admitted she was “gutted” after there was a wardrobe mishap during her routine.
Strictly Come Dancing continues on Saturday at 6.35pm on BBC One.