Although she was upset to be given the axe, Nancy, 52, paid tribute to her partner, saying she could not have down it without him.
She told co-host Brooke Burke: "I am so proud. I really cannot take the credit [for my performances]. It's been all Tristan from the get-go. It's been the whole crew at 'Dancing with the Stars'. It's been my whole family who took care of [my] twins so that I could dance."
She then looked poignantly at Tristan, touched his face and said: "But especially to you, Trist, I thank you."
Rob has now made it through to next week's semi-final, leaving his family thrilled.
Sister Kim wrote on twitter: "I truly can't express how proud I am of @RobKardashian & @CherylBurke 4 working so far 2 get 2 the semi finals! (sic)"
Khloe, 26, excitedly wrote: "OMG!!!!!!! Rob is safe!!!! Thank you so much for your support!!!! Wow!!!! This is amazing!!!!
"I love how he is improving and gaining confidence :). (sic)"