Substitute Marcus Rashford scored an injury winner as United finally broke through Hull's resilient rearguard to maintain our perfect Premier League start.
The 18-year-old- making his first appearance of the season- steered home from close range after excellent build up from Wayne Rooney to spark scenes of wild celebrations in the away end.
David Meyler had gone close in a rare Hull attack as they briefly threatened an unlikely smash and grab win but this was a deserved victory for the dominant visitors.
Rashford's intervention was the climax to a performance of persistence and intelligence from Jose Mourinho's men, who changed tack several times before finally breaking down a Hull side who defended magnificently.
Zlatan Ibrahimovic headed over the bar and then fired into the side netting, Wayne Rooney also went close while Hull threatened at the other end through Tom Huddlestone.
Curtis Davies epitomised his side's defensive display and denied Rooney on the line in the 37th minute after good work from Juan Mata, before Robert Snodgrass- later to leave the field injured- went close twice in quick succession on the cusp of the interval.
Abel Hernandez forced a smart save from David de Gea and Ibrahimovic then found the side netting from a tight angle having latched on to the skipper's clipped free-kick.
With the game still goalless after an hour, Mourinho felt a change of impetus was required and introduced Henrikh Mkhitaryan in place of Anthony Martial.
The Armenian threatened to find the breakthrough after a brilliant burst forward from his own half, but Hull continued to stand firm and almost stole a shock lead through Huddlestone's deflected shot which flew narrowly wide.
A further attacking threat was needed and duly arrived in the form of Rashford and, after Rooney and Paul Pogba had blasted off target from distance, the young striker's marvellous run and resultant shot forced a superb save from the sprawling Eldin Jakupovic.
Pogba again lashed narrowly wide with a 25 yarder, but it looked like Mourinho's men would have to settle for a point until the breakthrough finally arrived in the dying minutes.
Rooney's brilliance down the left saw him skip past Jake Livermore, slip the ball around Ahmed Elmohamady and cut the ball back for Rashford to ram in from three yards.
It was classic United and another memorable moment in the already exciting short career of the superb young striker.
Overall team performance: 7.5/10
United Faithful Man of the Match: Eric Bailly