Boro led twice in a lively first half but United equalised twice to make ir 2-2 at the interval.
Stephen Thompson gave Boro the lead inside ten minutes only for United to respond with an equaliser within 5 minutes. Boro replied almost immediately through Nathan Fisher and they held the lead almost until the break.
United took the lead with an hour gone and Boro gambled with three late substitutions but the home side hung on earn a quarter final tie against Liverpool.
Boro team:
Steele, Honeyman, Bennett (Hillerby), Langthorne, Johnson, Smallwood (Cronsberry), Franks, Robson, Thompson, Walker, Fisher (Martin)