Manchester United moved up to fifth in the Premier League as Middlesbrough’s first game since the departure of manager Aitor Karanka ended in defeat.
Ashley Young’s deep cross found Marouane Fellaini at the back post to head past Victor Valdes, before Jesse Lingard’s terrific strike doubled United’s lead after the break.
Boro, with head coach Steve Agnew in charge, were invited to apply pressure and when Chris Smalling made a mess of an easy clearance in the box, substitute Rudy Gestede pounced.
But former United keeper Valdes slipped in stoppage time and Antonio Valencia’s tap-in secured the three points.
Jose Mourinho’s side leapfrog Arsenal and Everton into fifth, while Middlesbrough remain 19th in the table and are five points from safety.
Having parted ways with Karanka on Thursday, Middlesbrough chairman Steve Gibson charged Agnew with helping the Riverside club avoid the drop.
But the former assistant manager was unable to inspire his side to a fifth Premier League win this season despite dominating possession for large periods of the game.
Alvaro Negredo looked isolated up front before Agnew introduced Gestede on 67 minutes, and with two in attack Boro looked capable of drawing level.
But United, showing seven changes from their Europa League win over FC Rostov in midweek, ground out a tricky three points.
Six hundred Premier League wins
This was Manchester United’s 600th victory in the Premier League – making them the first side to reach the landmark.
And while this was a notable moment for the club, their manager will surely be more concerned with their rise up the Premier League table and their ability to grind out a win without suspended top scorer Zlatan Ibrahimovic and injured record signing Paul Pogba.
United finish the day inside the top five of the Premier League table for the first time in 184 days.
And they are also on an 18-game unbeaten run in the competition stretching back to a 4-0 loss to Chelsea in October, but have only moved up two places, from seventh to fifth, during that spell.
They have finally moved away from sixth spot – a position they have made their own this season – and are now in a position to challenge for the top four.
New boss, same old Boro
Middlesbrough dominated possession in the first 15 minutes as they started the game on the attack.
But the lowest scoring team in the Premier League, with just 20 goals, once again failed to turn pressure into points.
Fresh from taking over from Karanka, Agnew made four changes, three of them in attack, from his side’s FA Cup defeat by Manchester City.
Gaston Ramirez, Stewart Downing and Alvaro Negredo replaced Adama Traore, Gestede and Cristhian Stuani – but Ramirez was the only player to force a save from United goalkeeper David de Gea in the first half.
And once Fellaini found the back of the net on 29 minutes, the stats looked even more grim for Boro.
Boro have gone behind 16 times this season, and only picked up two points from a losing position.
And the last time United lost a Premier League game having taken the lead was away at Swansea in August 2015.
Agnew’s side did produce a response once 2-0 down, with Gestede netting Boro’s first goal in eight and a half hours of football, but a lack of clinical finishing once again proved to be their downfall.
Gestede’s impact on the game also included a clash with United defender Eric Bailly which prompted a mass confrontation between the two sides, while the ill-feeling appeared to continue as the players headed for the tunnel after full-time.
Jesse Lingard was Man of the match