The TV entertainer and professional partner Iveta Lukosiute found themselves in the bottom two with Richard Arnold and Erin Boag.
The 14 couples had each danced a foxtrot, jive, cha cha cha, Viennese waltz or salsa, with the judges' scores combined with scores from last week and amalgamated with viewers' votes.
The bottom two couples performed their routines once more in the dance-off, with Arnold and Boag doing the cha cha cha to The B-52's 'Love Shack'. Ball and Lukosiute performed the foxtrot to Michael Bublé's 'Everything' in order to stay in the competition.
Judge Craig Revel Horwood told the couples: "I would like to save, based on content alone, Richard and Erin."
Darcey Bussell also chose to save Arnold, saying: "For me, it is about the dance content between the two dances, and who gave me the most confidence in them, and for me that is Richard and Erin."
Also selecting to save Arnold, Bruno Tonioli said: "For both couples it wasn't as good the second time round. Again, for content alone, for that reason I would go for Richard and Erin."
The result meant that Johnny Ball and Iveta Lukosiute - who took over from the injured Aliona Vilani - would leave the BBC show.
Johnny Ball said of the results: "I think for my age I did quite, quite well. I'm so disappointed I'm leaving, I really, really am."
Strictly Come Dancing continues with a Hollywood-themed show on Saturday, October 20 at 6.30pm on BBC One.