They faced former England rugby star Chris Robshaw and Nadiya Bychkova in the dreaded dance-off, performing a salsa to Bonkers by Dizzee Rascal.
Head judge Shirley Ballas, Anton Du Beke, and Craig Revel Horwood all voted to save Robshaw and Bychkova, with Motsi Mabuse also agreeing with the decision.
Skinner expressed his enjoyment despite his short time on the show, while Dowden thanked him for helping her regain confidence after her recent cancer treatment and foot injury.
Skinner had previously faced controversies, including snatching a journalist's phone and admitting to cheating on his wife, and had linked viewer backlash to his support of the US president.