Following the public vote, the gold-medallist swimmer, 24, faced singer and actress Toyah Willcox, 66, in the dance-off.
Donning sparkly and fringed outfits, Dean performed his energetic cha cha with his professional partner Nadiya Bychkova to Boogie Wonderland by Earth, Wind & Fire once again.
He kicked off the live show on Saturday with the routine, receiving a score of 20 from the judges and bringing his total to 43 after picking up 23 points last week for his tango to Harry Styles’s song Golden.
Meanwhile, Willcox and professional partner Neil Jones reprised their lively jive to Nutbush City Limits by Ike & Tina Turner.
They picked up 18 points for their effort but they still remained at the bottom of the leaderboard with a total of 30 after they placed at the bottom last week with a score of 12.
After both couples danced a second time, the judges delivered their verdicts, with Craig Revel Horwood and Motsi Mabuse both choosing to save Willcox and Jones while
Anton Du Beke opted to save Dean and Bychkova.
Head judge Shirley Ballas had the deciding vote and chose to save Willcox and Jones.
Reflecting on his time on the show, Dean said: “I’ve had the best time the last few weeks and getting to work with Nadiya has been incredible.
“I wish I could have gone further and done more dances.
“I’ve had the most fun and I wish we could keep going longer and longer. We’ll still go out for loads of brunches I’m sure.”
His dance partner Bychkova said she discovered Dean is not just a three-time Olympic champion but a “true gentleman”.
“He taught me how to work really hard and how to put everything in”, she added.
“And you know what? On this programme, sometimes to win, you don’t need to win, and that’s how I feel this year.”
The first results show of the series also saw the professional dancers and judges perform an “avant-garde gothic tango” routine to Prince’s When Doves Cry and New Order’s Blue Monday.
Jazz group Ezra Collective also performed a rendition of God Gave Me Feet For Dancing featuring Yazmin Lacey.
The remaining 14 couples will take to the dancefloor next Saturday for the movie week special on Saturday October 5 at 6.25pm with the results show on Sunday October 6 at 7.15pm on BBC One.