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This was Marouane Fellaini's first Premier League goal of the season

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

Mourinho 'super happy' after win

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.

Agnew praises 'excellent' Boro attitude

Man of the match - Jesse Lingard

Jesse Lingard unleashed a fierce shot from 25 yards that curled into the top corner to give United a crucial 2-0 lead

What they said

Middlesbrough head coach Steve Agnew: "If we show that commitment and that sort of intensity until the end of the season then we have a real chance of staying in this league.

"It is a relief to get a goal and I felt that when we got that goal, we had Manchester United defending in the box for their lives and again we didn't quite get the bounce of the ball to get the equaliser, which on the balance of play I thought we deserved.

"I know that we will take that fighting spirit for the rest of the season."

Manchester United manager Jose Mourinho: "[I applaud] our attitude and desire and our way of thinking. We don't have plan B, C, D, E, F and G - but we have M, N, O, P and S.

"It is fantastic because we manage in the same week, to go to the quarter-finals of the Europa League which is an important target for us.

"At the same time, we got these three points that keep us in the race for the fourth position so we still have two doors for Champions League football next season.

"These guys gave everything, we started the game really well. Valdes made three fantastic saves before our first goal. We controlled everything until our second goal."

What's next?

The Premier League takes a break for the next round of World Cup qualifiers, after which both Middlesbrough and Manchester United face hectic April schedules.

Middlesbrough

Middlesbrough have six games in the packed month, but the next two games could define their season.

On Sunday, 2 April (13:30 BST) they travel to relegation rivals Swansea before another away trip to Hull City three days later (19:45 BST).

Swansea sit five points above them, just outside the relegation zone in 17th, with Hull in 18th, two points adrift of Middlesbrough.

Manchester United

United host West Brom in the Premier League - the first of eight fixtures in April as they chase Europa League success and a top-four finish.

April 2017 fixtures (all times BST) Premier League West Brom (H) Sat 1 April, 15:00 Premier League Everton (H) Tue 4 April, 20:00 Premier League Sunderland (A) Sun 9 April, 13:30 Europa League quarter-final Anderlecht (A) Thu 13 April, 20:05 Premier League Chelsea (H) Sun 16 April, 16:00 Europa League quarter-final Anderlecht (H) Thu 20 April, 20:05 Premier League Burnley (A) Sun 23 April, 14:15 Premier League Swansea City (H) Sun 30 April, 12:00

Mourinho criticised the Premier League during the week, bemoaning their fixture schedule and reluctance to aid clubs competing in Europe.

But United are no strangers to a busy back end of the season.

Both the 2008-09 and 2010-11 campaigns, under Sir Alex Ferguson, also featured eight April fixtures.

They lifted the Premier League title in both seasons, despite two semi-final exits in the FA Cup and losses to Barcelona in Champions League finals.

And back in 1999, 14 games in 54 days were the climax to the most successful season in their history as United secured the FA Cup, Champions League and Premier League Treble.

Fellaini finally nets - stats

This was Middlesbrough's 1,000th top-flight league defeat; the 14th team to reach this tally.

Lingard scored his fifth Premier League goal for United - still one fewer than he has collectively in other competitions (one in the Community Shield, two in Europa League, one in EFL Cup, two in FA Cup).

United have scored more goals from outside the box in the Premier League this season (six) than they did in 2015-16 (five).

Fellaini's strike ended his run of 30 Premier League appearances without a goal.

Thirteen of Fellaini's 33 Premier League goals have been headers (39%).

Gestede's goal was the first Middlesbrough have scored in the Premier League in 509 minutes of action.

This was the first time Mourinho has started a league game with a three-man defence since 15 May 2011 (Villarreal 1-3 Real Madrid in La Liga).