"Brighton deserved more than they got," United's manager Jose Mourinho told Sky Sports. "They played really well and when they had the ball they were dangerous."
In Saturday's late game a strange 85th minute goal from Brazilian Willian earned champions Chelsea a 1-1 draw at Liverpool after Mohamed Salah's 15th goal of the season looked to have given the hosts the three points.
Just two minutes after coming on as a late substitute at Anfield, Willian whipped in an attempted cross from the right which floated over Liverpool keeper Simon Mignolet and into the net.
In London, Harry Kane scored his 40th goal of the year to salvage a 1-1 draw for Tottenham Hotspur against managerless West Bromwich Albion at Wembley.
Salomon Rondon handed the visitors a fourth-minute lead by outmuscling Davinson Sanchez and rolling a low shot past Hugo Lloris.
Tottenham dominated possession but looked unlikely to score against a well- drilled Baggies team until Kane steered home Dele Alli's cross in the 74th minute.
West Brom, who had Gary Megson in caretaker charge following Tony Pulis's sacking last Monday, remain 17th in the standings, one point above the relegation zone.
The remainder of Saturday's early action concerned the bottom end of the Premier League table, with Crystal Palace picking up a vital home win over Stoke.
Mamadou Sakho's stoppage-time winner gave Palace a 2-1 victory and moved them within three points of safety, just one behind Swansea who drew 0-0 with Bournemouth.
"That goal is worth its weight in gold," said manager Roy Hodgson.
Watford continued their impressive form under Marco Silva with a 3-0 win away to Newcastle which keeps them in eighth, five points clear of nearest rivals Brighton.