Noble effort as Cats hold Toffees.
A handball decision gave Everton a first-half penalty, but Sunderland keeper Trevor Carson saved Jose Baxter's spot-kick.
And Noble punished that miss when he fired the Black Cats in front a minute before halftime.
Everton levelled through Cody Arnou eight minutes into the second period.
Sunderland's Scotland international defender Russell Anderson was included in the starting line-up and played the first 45 minutes as he continued his rehabilitation from a longterm knee injury.
SUNDERLAND: Carson, Kay, Brown, Reed (Liddle 74), Anderson (Tounkara 46), Cornforth, Weir, L Noble, O'Donovan, R Noble, Meyler.
EVERTON: Nash, Coleman, Bidwell, Peterlin, Duffy, Mustafi, Donegan (McAleny 81), Forshaw, Arnoux, Baxter (Akpan 66), Craig.
REFEREE: Mr Adcock