Neighbours Edenderry inflicted Rhode's first defeat in the round-robin series of the Offaly SFC since 2001 last Saturday.
The three-in-a-row county champions' remarkable record came to an end at the first hurdle at home in Fr Dowling Park.
Lining out without key players Brian Darby and Conor McNamee, Rhode fell to a two-point defeat at the hands of their near rivals.
Elsewhere, last year's intermediate champions Shamrocks defeated Gracefield, Clara overcame Ferbane and Tullamore beat Cappincur.
Offaly SFC first round results...
Edenderry 0-13 Rhode 0-11
Shamrocks 2-14 Gracefield 1-14
Clara 1-13 Ferbane 0-11
Tullamore 2-11 Cappincur 0-7