Steve Cotterill's men have been rewarded for their victory over Peterborough on Saturday with a home tie against Tony Mowbray's Black Cats - who currently sit 15th in the Championship.
It will be Salop's sixth straight season in the third round of the FA Cup - and comes a season after they went to Liverpool at the same stage last season.
Elsewhere, Wolves will travel to Anfield to take on the Reds in an all Premier League tie.
West Brom are facing an away non-league trip as they get set to take on National League high flyers Chesterfield - with Aston Villa facing Stevenage at Villa Park.
And National League side Wrexham have been handed a big away tie as they take on Championship side Coventry City.
All ties will be played on the weekend of January 6 and January 9.