The defeat was harsh on an assured and enterprising Brighton side, but that will be of little consequence to Jose Mourinho as United recorded an 11th straight home win across all competitions.
After wasting numerous first-half chances in Wednesday's 1-0 Champions League loss at Basel, United could not even be accused of profligacy on this occasion as the likes of Anthony Martial, Paul Pogba and Marcus Rashford largely struggled to carve out opportunities for Romelu Lukaku.
Mat Ryan produced an excellent double save to thwart Lukaku and Pogba on the stroke of half-time but the goalkeeper could do nothing to keep out the winner midway through the second half as Ashley Young's shot from 20 yards looped up wickedly off Dunk and dipped just below the crossbar into the top-right corner.
Defeat ended Brighton's five-match unbeaten run but Chris Hughton's side can at least console themselves with a performance that showed ample promise as they sit safely ensconced in mid-table after 13 matches of their debut Premier League campaign.
The tone for an even encounter was set inside the first five minutes as both sides created openings.
Lukaku blazed over having exchanged passes with Martial before Anthony Knockaert got in behind the United defence only to fizz a cross-cum-shot across the face of goal.
David de Gea comfortably held Pascal Gross' effort from the edge of the box as the Seagulls continued to play with plenty of poise while United were restricted to half chances, Lukaku stretching to nod Antonio Valencia's cross wide 10 minutes before the break.
Brighton had Ryan to thank for going into half-time level, however, the goalkeeper saving superbly from Lukaku's back-post header before denying Pogba's rebound from point-blank range.
United dominated possession after the interval without threatening Ryan's goal, Mourinho introducing Zlatan Ibrahimovic just after the hour and in the 66th minute the deadlock was broken thanks to Young's sizeable slice of fortune.
Knockaert continued to pose a threat, whipping a low ball across the face for a second time in the match and Gross was close to getting a telling touch on Bruno's devilish delivery from the right.
Shane Duffy headed wide with four minutes remaining and the centre half was perhaps fortunate to only see yellow for a scything challenge on Ibrahimovic as United - who are unbeaten in 39 home matches in all competitions - held on to remain in touch with City at the top.
Key Opta stats:
- Manchester Utd have gone 39 games in all competitions without defeat at Old Trafford (W28 D11), last losing to Man City in Sept 2016 – 441 days ago.
- The Red Devils have lost just once in their last 48 Premier League home games against newly-promoted teams (W41 D6 L1) – with that defeat coming against Norwich City in December 2015.
- Brighton have never won away against Manchester United in any competition (D2 L7).
- Manchester Utd have conceded just six goals so far this season, their lowest total after the first 13 league games of the season since 2007-08 (6).
- Jose Mourinho’s side have recorded a clean sheet in 26 of their 51 Premier League matches since the start of last season; more than any other side.
- Lewis Dunk is the first player in Premier League history to score an own goal versus both Manchester Utd and Manchester City in the same season.
- Paul Pogba attempted more passes versus Brighton (110) than in any other Premier League match in his career.