Ole Gunnar Solskjaer became the first Manchester United manager to win his first six league games in charge as his side held on to beat Brighton.
It was United's seventh straight win since the Norwegian took over at Old Trafford on an interim basis a month ago and they are now just three points off fourth-placed Chelsea, who play Arsenal in Saturday's late kick-off.
Paul Pogba put United in front after winning and then converting a penalty in the 27th minute.
Marcus Rashford doubled the lead just before half-time with a beautiful solo goal on his 150th appearance for the club.
Pascal Gross halved the deficit for the visitors when he scored in off the bar with just over 20 minutes remaining.
Brighton improved in the second half but their wretched away record continued as they fell to a fifth defeat in their last eight Premier League games.
United's winning streak continues
The last time these sides met was in August, when United's season under Jose Mourinho began unravelling with a 3-2 defeat.
But United's first-half performance at Old Trafford on Saturday was worlds apart from that game last summer.
Solskjaer almost had the luxury of naming an unchanged line-up for back-to-back league games for the first time since December 2017, but Luke Shaw fell ill in the warm-up and Diogo Dalot took his place.
United put Brighton under relentless pressure from the off and deservedly took the lead.
Nemanja Matic's cross-field pass found Pogba, whose first touch took him past Gaetan Bong and the defender then clumsily nudged him over.
The Frenchman's stuttering penalty run-up has not completely disappeared, but this was nowhere near as long as his 26-step effort against Everton back in October and he slotted his shot past David Button.
Rashford's recent goalscoring form continued as he got his ninth of the season and his fifth under Solskjaer.
The England striker was played in by Dalot, sent Gross the wrong way and then bent his shot into the top corner.
Rashford was excellent for the first hour, spraying passes about with confidence and whipping in a stunning cross for Jesse Lingard, who prodded wide when he really should have scored.
They should have had more to show from their 20 attempts, but only five were on target, with Pogba and Anthony Martial guilty of missing chances.
United eased off in the final 20 minutes, lacking sharpness and became sloppy as they missed out on a fourth clean sheet in a row.
“Today we were tested,” said Solskjaer. “I didn't think we played the game out as we should have. That's perhaps the next challenge for the boys.
“Sometimes you make it hard work. I thought we played some greats stuff at times. At the start of the second half we could have finished the game with great chances.
“The last 20 minutes we were in trouble. You can't always play fantasy football. At times we did and it's a great three points.”
More away day blues for Brighton
Chris Hughton's side have won eight points away from the Amex Stadium this season and have just four away wins since joining the Premier League last season.
They particularly struggle against the top sides Following last week's defeat by Liverpool and Saturday's loss at Old Trafford, they have now lost all nine of their Premier League away games against ‘big six' sides by an aggregate score of 19-2.
The first half against United proved damaging, as they rarely threatened and struggled to cope with the hosts' forward line.
A double change on the hour mark with the introductions of Florin Andone and Anthony Knockaert provided the attacking impetus the Seagulls needed.
Davy Propper did well to create Gross' goal, flicking a pass with the outside of his boot over the head of Victor Lindelof to the German, who chested it down and fired his shot off the bar and in.
Brighton finished the stronger, their attacks and crosses sparking panic in the United team, but it came too late.
“The biggest disappointment is the goals we conceded,” said Hughton. “I thought we very much gave them a game.
“We will need lots of that come the end of the season but I thought there was a chance for us today.
“We needed a bit more quality in the final third and in general.”
Asked about bringing players in January, he added: “You can never say never but I don't think it will be the case. Possibly one or two will be going out on loan.”