Strictly contestants have remained in the competition, despite days of controversy after they were photographed kissing in the street.
Jones is married to another dancer on the show, and Walsh was in a relationship at the time.
They finished in the top half of the leaderboard on Saturday night after receiving 28 points from the judges for their Charleston.
It was one of the highest scores of the night, putting them in fourth place overall.
Those points were then combined with votes from the public.
Katie Piper and her professional partner Gorka Marquez became the third couple to leave the show this year.
Following the cheating revelations, Walsh was publicly dumped by his long-term girlfriend.
Rebecca Humphries released a statement accusing the comedian of "controlling" and "aggressive" behaviour in the run-up to the kiss, which occurred on her birthday.
Both Walsh and his dance partner apologised for their actions, which prompted speculation they might leave Strictly Come Dancing.
However, they stayed in the competition and 11.9 million viewers tuned in to watch them dance to Bills by Lunchmoney Lewis.
Earlier in the week, judge Craig Revel Horwood labelled it their "Dance of Shame".
No overt reference to the scandal was made during the Saturday night show and the couple received cheers from the audience as they attempted tricky lifts, including one where Jones stood on Walsh's shoulders.
The judges were largely impressed, with head judge Shirley Ballas saying the "whole routine was totally entertaining, you got one tiny kick wrong in the middle, but I loved it".
Some fans writing on social media felt Walsh and Jones had been through the wringer enough following their kiss.
"I have never voted on @bbcstrictly but tonight I will be voting for @Mrs_katjones and @seannwalsh. What happened has nothing to do with the show and they don't deserve to end their journey under a cloud like this," wrote a viewer named Charlotte.
Andrew Robert Lee said: "Considering what a difficult week Seann and Katya have had and how awkward dancing that must have been in front of a live studio and TV audience I’d have given them 10."
However, others felt the pair had been over-marked in a bid to keep them in the show.
Holly Grinter wrote: "Completely over marked!!! Riddled with mistakes."
Another viewer, Hayley Parry-Dafis, said: "It's just to keep them out the bottom two to keep the ratings."
Nicola Kirkland wrote: "Judges have over-marked as the only hope of them staying in is to be higher up the score board."
Hosts Claudia Winkleman and Tess Daly made a light-hearted reference to the affair as they opened the show.
Daly told the audience: "For the last seven days, our couples have been eating, sleeping, breathing, dancing."
Winkleman said: "Apart from that, it's been a quiet week," to which Daly added: "Other than the odd headline."
An inadvertent joke appeared to have been made when a subtitle mistake happened during the duo's debrief of the judges' marks.
As the pair reflected on being awarded a six, the subtitle read: "You look so happy with that sex and then…"
Documentary maker Stacey Dooley and her partner Kevin Clifton topped the leaderboard with their foxtrot, which was highly praised by the judges and saw them take their first nine of the competition.