Two goals from summer signing Paul Wheatcroft netted twice, while Martin Carruthers got the thrid strike.
It was the most competitive game United have faced in pre-season, and played at a faster tempo than any of the other games.
Grantham lined up with four former Irons - Gary Bull, Jimmy Neil, Lee Marshall and Mario Ziccardi.
Matthew Sparrow returned from inury to make his first half hour appearance of the pre-season, he also featured for a full 90 minutes in a practise match this morning.
It was only the Iron's second win on English soil since last season, and marked a significant increase in confidence as shown by comments made by Basque midfielder Alex Calvo-Garcia after the match.
"I think we have been improving on each game we play and last night was more like what we're going to find in the season," said Alex Calvo-Garcia.
"Playing against Coventry and Derby is a good fitness test but is not really what we're going to find in the third division."
Speaking to the club's Ironworld subscription service assistant manager Russ Wilcox stated that he hoped the goals will hand Paul Wheatcroft a massive boost ahead of the season.
United will begin their defence of the trophy in just eleven days time, when they make the short trip to Gainsbrough Trinity in the first round of the 2002-03 competition.