The 18-year-old - making his first appearance of the season - steered home Wayne Rooney's cross to spark wild celebrations on the away bench.
Moments earlier, David Meyler had blazed over in a rare Hull attack.
But it was a deserved win for United who had gone close though Rooney, Zlatan Ibrahimovic and Paul Pogba.
They and Chelsea are the only Premier League sides with a 100% record from three games with Manchester City - with two wins from two games - playing West Ham on Sunday.
United find a way
Rashford's winner was the climax to a performance of persistence and intelligence from the visitors who changed tack several times before eventually breaking down Hull.
Ibrahimovic arrived at Old Trafford with a reputation for audacity, but, in the first half, it was his physical size rather than mercurial skill that posed most threat.
Offering himself as a constant target in the box, the Swede headed just over the bar in the 10th minute before an extravagant backheel found the side-netting.
The excellent Curtis Davies blocked the more direct route to goal after the break, but the guile of Henrikh Mkhitaryan and the pace of fellow substitute Rashford stretched the Hull defence in different directions and, finally, beyond breaking point.
Source: BBC Sports
Source: BBC Sports
