North End have a poor record at Barmall Lane apart from a victory last season in the league. Preston started the stronegr but it was the hosts who took the lead through Jamie Murphy before the break.
It seemed like Preston's poor form was to continue until a ten minute period midway through the second half when they stunned Sheffield United with three goals.
Gallagher scored from a free kick before Huntington headed home from a corner to give Preston the lead. Humphrey was then fouled in the box with Gallagher converting the penalty.
Pretson now face Manchester United at home in the next round on 16 February 2015 with the match to be screened live on BBC television. It is the first time that the teams have clashed since 1972 when Preston lost in the FA Cup.