Man United climbed to sixth as two goals from Scott McTominay proved enough to beat Chelsea 2-1, with the Blues languishing in tenth.
United got off to a strong start in the game and had a great chance to open the scoring as they were awarded a penalty in the seventh minute after a foul against Antony.
Captain Bruno Fernandes took the spot kick but saw his effort saved before Rasmus Hojlund fired his follow-up effort well over the bar.
In the 19th minute, after a mistake by Nicolas Jackson to give away possession, McTominay got on the end of Harry Maguire's blocked shot and was able to fire his effort past Sanchez, opening the scoring for the hosts.
United controlled most of the half but in the 45th minute, against the run of play, Cole Palmer found space to shoot after beating Victor Lindelof and placed his shoot in the bottom far-right corner, giving Andre Onana no chance of keeping it out, not aided by his positioning, as Palmer drew the sides level.
Man United continued to dominate most of the second half, despite Chelsea starting well, and eventually took the lead in the 70th minute as McTominay got his second of the night after heading home from Alejandro Garnacho's cross, which would prove enough to seal the win for the Red Devils.
Story of the game
Following the weekend's defeat away to Newcastle, Ten Hag made four changes to his starting line-up, which included the omission of Marcus Rashford, who was replaced in the team by Antony.
His dropping comes amid fierce criticism from fans over his recent performances, which have seen him score just once, from a penalty, in his last ten games for club and country, and just three times all season.
Pochettino made just two changes to his Chelsea side that beat Brighton at the weekend, with Marc Cucurella and Cole Palmer replacing Benoit Badiashile and the suspended Connor Gallagher in the starting line-up.
Reece James was only fit enough to start on the bench after suffering from knee pain in the lead-up to the game.
Man United started the game on the front foot and were piling early pressure on the Chelsea defence and looked incredibly threatening with almost every touch of the ball.
The drama started just seven minutes into the game when, after a brief VAR check, the hosts were awarded a penalty after Enzo Fernandez seemingly stood on Antony inside the penalty area.
Club captain Fernandes stood up to take his penalty, but saw it saved by Sanchez, with Hojlund firing his follow-up effort after the save well over the crossbar.
It was just minutes later that Jackson played Mudryk in behind the United defence, but the Ukrainian failed to get his shot on target as it rocketed into the side netting.
A short while later, McTominay opened the scoring for the hosts after firing home from Maguire's blocked shot, which came after Jackson gifted Ten Hag's side possession in the build-up.
From here Chelsea began to grow into the game, but chances were still few and far between for Pochettino's side, as their frustrations grew.
Sanchez made a sensational double save in the 32nd minute, as McTominay looked to grab his, and United's, second of the evening. The Scotsman fired a close-range header straight at the 26-year-old, before he fired his follow-up effort straight at him too, though the Spaniard still did very well to keep it out.
Just a minute later Chelsea had a huge chance to level things up as Sterling and Jackson charged towards the United goal unopposed but, after Sterling laid it into the Senegalese striker, he squandered the chance and Onana was able to comfortably collect the ball.
As half-time loomed, Ten Hag's side regained control of the game and looked very threatening once more, with Chelsea making sloppy mistakes and gifting chances to the hosts.
Despite this, Palmer received the ball on the edge of the box in the 45th minute, where he was able to beat Lindelof and place an admittedly weak effort across the face of goal into the far bottom right-hand corner - well out of the reach of Onana.
After some lengthy injury time, owing to the VAR stoppage and McTominay requiring some fairly lengthy treatment, the referee brought the first half to an end and the teams went into the break level.
Chelsea started the second half much better than they had the first, but were still struggling to create meaningful chances while they had possession.
Their positive spell would soon end as United regained control of proceedings and they almost found a goal to put them ahead through Garnacho but the Argentine dragged his curling effort just wide of the far post.
A short while later, in the 61st minute, a good chance fell for Antony near the edge of the box, but the Brazilian saw his effort deflected behind for a corner - which came to nothing.
A moment later saw fierce penalty appeals for Ten Hag's side after calls for handball but, after a VAR review, the officials determined that there was nothing untoward and play resumed at 1-1.
It would not be long, however, before McTominay got on the end of a cross from Garnacho at the far post and headed home his second goal of the night, to once again give Man United a thoroughly deserved lead.
Immediately after kick-off, United looked to attack from the off in a bid to double their advantage, but Chelsea just about shut them out and kept the deficit to one.
The hosts continued to control the game from here on out but were made to survive a very late onslaught of pressure from Chelsea late on, but their efforts were not enough to rescue a draw, with the referee drawing proceedings to an end with Man United taking a much-needed three points, while Chelsea's problems continue.
Player of the match - Scott McTominay
McTominay was undoubtedly the standout in this game, with his two goals being the difference for Man United as they overcame an underwhelming Chelsea side who seemed to lack any real creativity.
The Scotsman took his two goals excellently and, on another day, could have had a hat-trick with some of the other chances that fell for him.
Aside from his goals, the 26-year-old had a very good all-round game, which included boasting a 95% pass success rate - though he will definitely look back in despair at his three missed big chances.