Mellor and his partner Nancy Xu performed the Jive this week to Ricky Martin's Livin' La Vida Loca, and were awarded 8s from Craig Revel Horwood and Shirley Ballas, while Motsi Mabuse and Anton Du Beke awarded the pair with 9s.
Meanwhile Yassin and his partner Jowita Przystal performed the Foxtrot to Islands In The Stream by Dolly Parton and Kenny Rogers. Craig and Anton awarded the pair with 8s, with Shirley and Motsi awarding 9s.
It means both couples have tied the scores of the pair who topped the leaderboard in week 1 last year, AJ Odudu and Kai Widdrington.
After receiving the judges comments Mellor said: "When I first saw that routine I said there's no chance I'll be able to do it, there's no point, we'll have to pick another dance. And after 10 days of being tortured from the feet up she's [Nancy] got me to that stage and it's all down to her, she's unbelievable, I'd be nothing without her."
Meanwhile Hamza said: "Jowita's absolutely amazing, she's been working me so hard and it's all paid off when the judges are saying all those amazing comments - it's all thanks to her."
This season's first live show came a day after the launch show, which saw this year's pairs announced, including two same-sex couples.
Other impressive scores in this year's first live show were achieved by Molly Rainford and Carlos Gu dancing the Samba to Kiss My (Uh Oh) by Anne Marie and Little Mix (31) and Fleur East and Vito Coppola with the Cha Cha Cha to Let's Get Loud by Jennifer Lopez (29).
Strictly Come Dancing airs on BBC One on Saturdays and Sundays.
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