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A point leaves United still down in 13th, six points off the top four.
Moises Caicedo’s strike denied Manchester United victory in their first Premier League game since sacking Erik ten Hag as Chelsea claimed a 1-1 draw at Old Trafford.
Interim boss Ruud van Nistelrooy, who will be replaced by Ruben Amorim later his month, sprinted down the touchline in celebration after Bruno Fernandes put United in front from the penalty spot 20 minutes from time.
Caicedo quickly replied for the Blues, who edge above Arsenal on goal different into fourth.
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A point leaves United still down in 13th, six points off the top four.
Amorim was not in attendance as he prepares to take charge of Sporting Lisbon for the one of the final times against Manchester City in the Champions League on Tuesday.
United were far more competitive than in 3-0 demolitions by Liverpool and Tottenham at home this season, but showed many of the same flaws that cost Ten Hag his job.
Van Nistelrooy enjoyed a 5-2 demolition of an under-strength Leicester in his first match in charge to reach the League Cup quarter-finals in midweek.
Still a hero among the United fans from his days as a prolific striker, the Dutchman’s name was chanted in a buoyant pre-match atmosphere.
However, a Chelsea side that have lost once in nine Premier League games, provided a much stiffer test for a United side still short on confidence.
Noni Madueke came closest to opening the scoring for Chelsea in the first-half when he headed Cole Palmer’s corner off the post.
It took United time to find their feet as an attacking force but they were unfortunate not to go in front just before half-time.
Marcus Rashford hit the crossbar with a cushioned volley in the last action of a disappointing first 45 minutes from both sides.
Pedro Neto’s burst of pace nearly gave Chelsea a dream start to the second period but the Portuguese winger’s shot flew just past the far post.
The Blues remain overly reliant on Palmer for inspiration.
The boyhood United fan, who began his career at Manchester City before joining Chelsea last year, was kept quiet by Van Nistelrooy’s pairing of Casemiro alongside Manuel Ugarte in midfield.
Before kick-off only Southampton had scored fewer than United’s eight Premier League goals in nine games this season.
The lack of efficiency in front of goal that Ten Hag often bemoaned was in evidence again.
Garnacho wasted a glorious chance to open the scoring from Fernandes’ cut-back with a tame effort that looped into the arms of Sanchez.
United were gifted the chance to break the deadlock when Robert Sanchez clipped Rasmus Hojlund inside the box.
Fernandes kept his cool to send the Spanish international goalkeeper the wrong way and spark wild celebrations from Van Nistelrooy.
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United’s joy was short-lived as Chelsea hit back within four minutes.
A corner was only cleared to the edge of the box, where Caicedo connected a sweet strike to fire into the bottom corner.
Chelsea should have struck again moments later when substitute Enzo Fernandez spooned over with Andre Onana stranded.
It was United who came closest in a frantic finale when Garnacho’s acrobatic effort flew just over.