The Welsh classical singer wowed the judges as she performed the foxtrot with her professional dance partner Mark Ballas.
Katherine looked incredible in a floor-length canary yellow gown, and long, white, satin gloves both adorned in sparkles.
Judge Carrie Ann Inaba sang Katherine's praises, saying: "You were fabulous! Best first dance on the first episode ever! Really, amazing."
As the singer received such high praise, she became visibly emotional. Judge Bruno Tonioli was also amazed: "That was exquisite. The style was impeccable. The quality of movement is... surreal."
He then warned Katherine that he would be expecting big things from her from now on: "Week one, where are we going to go from here? You're setting the bar so high, that really you have a lot to live up to."
The pair achieved a total of 26 points from the judges out of a possible 30, which was a tie with Family Matters star Jaleel White and his professional partner Kym Johnson.
After the show, Katherine tweeted her excitement: "OMG 2 9's & an 8! Joint top of the leader board! Just called my mum in Wales at 3 am to break the news #TellMeImNotDreaming".