Adams and Jones did a quickstep to the song “Get Happy”, a song most associated with Judy Garland who performed it in the 1950 film Summer Stock.
Judge Motsi Mabuse said she had been looking forward to seeing what the pair would come up with.
“I have to say I was very curious, ‘How is it all going to happen? How is it going to turn out?’” she said.
“And you haven’t disappointed me… We loved it, keep going.”
Craig Revel Horwood said the dance was “absolute dynamite”, while Shirley Ballas said Jones was a “genius” for coming up with the choreography.
The three judges awarded the pair a total of 21 points.
“Loving everything about #strictly this year, from Jacqui Smith (thank god, for once someone I recognise) to Bill Baiey in a headband to Nicola Adams making a tiny bit of history,” one fan wrote.
“It made me cry happy tears,” another viewer said of Adams and Jones’s performance.
“Glorious," another tweeted.
Elsewhere on the show, ex-home secretary Jacqui Smith languished at the bottom of the leaderboard after performing a foxtrot with Anton Du Beke.
EastEnders star Maisie Smith and Gorka Marquez performed a samba, scoring 24 points.
Made in Chelsea’s Jamie Laing returned after being forced to drop out of last year’s series due to an injury, and was first to dance live on the 2020 series.
However, he received mixed reviews from judges, with Revel Horwood criticising his performance as “flat-footed, very tight and restricted”.
“That might have something to do with those lovely trousers you are wearing, don’t leave much to the imagination do they!” he observed.
Singer HRVY and Janette Manrara closed the show with a jive and shot straight to the top of the leaderboard, with 25 points.
Mabuse said it “was the best first dance I have ever seen”.
Actor Caroline Quentin was emotional after performing the American Smooth with her professional partner Johannes Radebe.
Good Morning Britain presenter Ranvir Singh also impressed the judges, scoring 21 points.
Also competing were TV presenter JJ Chalmers, BBC presenter Clara Amfo, The Wanted singer Max George, former NFL star Jason Bell and comedian Bill Bailey.
A celebrity will not be voted out until next week.