Leeds will face the winners of a replay between the sides after National League club Eastleigh held Bolton to a 1-1 draw at the Silverlake Stadium on Saturday.
Eastleigh were on the verge of a huge upset and led 1-0 on a rain-ravaged pitch until Darren Pratley rescued Bolton with an 87th-minute equaliser.
Leeds’ last meeting with non-league opposition in the FA Cup ended in a grim defeat to Histon during Gary McAllister’s reign as manager in December 2008.
The meeting with Eastleigh or Bolton will take place on the weekend of January 30.