Marc Cucurella gave Chelsea a lifeline against Manchester United as his header was enough to secure three points and move the Blues back into the top five.
The match was an even and physical affair, with United pressuring their opponents early and defending well as they looked to earn a point away from home.
There were VAR checks in both halves - Harry Maguire had a goal ruled out for a narrow offside, and Tyrique George had a penalty disallowed after appearing to collide with Andre Onana.
Ruben Amorim will have wanted to take at least a point away from his opponents, as his side pick up their eighteenth defeat of the season despite having moments of dominance.
An eventful final weekend in the league now awaits - Chelsea could seal top five with a result against Nottingham Forest, whilst United could help out the Blues if they knock points off their opponents, Aston Villa.
Story of the Match
Enzo Maresca had started to find some consistency in his team lineups, but was forced into three changes for this game, with Reece James, Tosin Adarabioyo and Tyrique George all coming into the starting lineup.
Manchester United head coach Ruben Amorim will have part of his focus on next weeks Europa League final against Tottenham, but still showed desire to win - despite their league position being all but confirmed.
Suspension to striker Nicolas Jackson left Maresca with limited options - Tyrique George led the line, with Cole Palmer and Enzo Fernandez positioned close as attacking midfielders.
Noni Madueke and Pedro Neto occupied the wings, with Jadon Sancho ineligible to start for the Blues. There was very little attacking depth on Chelsea's bench, so they would need to make the most of their chances.
Madueke had the first real chance of the first half, sneaking in at the far post after a cross by Neto, but blazing the resulting effort high and wide.
United had attacking threats of their own: ex-Chelsea player Mason Mount came into the game following a good run of form, and received a warm welcome by the home crowd in the form of boos.
Their system allowed for several players to bomb forward and overload the defence, with Bruno Fernandes dictacting the play from a deeper midfield position.
The Blues were dealing with some early United pressure well, but struggled to build out from the back due to effective pressing by their opponents - with some physical challenges thrown into the mix.
Their blushes were spared as an early Harry Maguire goal was ruled out by VAR. The United captain had pounced on a Bruno Fernandes cross, but mistimed his run by the finest of margins; his shoulder was deemed to be in an offside position.
It was a huge let-off for Chelsea, who were sloppy and casual in their half of the pitch, giving themselves unneeded defensive work.
After a nervy opening, Reece James nearly gave his team the lead in spectacular fashion, with a long range strike clipping the outside of the post.
Moments later, Enzo Fernandez believed he was deserving of a penalty after his volleyed strike struck Rasmus Hojlund on the hand - but referee Chris Kavanagh waved away the appeals.
Chelsea had woken themselves up, however, and were beginning to create some more concrete chances in United's half.
They had done well to nullify some threats, too: Amad Diallo was having no luck down the right hand side, while Rasmus Hojlund was being shut out of the game well by Tosin.
United were defending well, but they were being forced backwards, with every attempt to clear the ball resulting in a turnover of possession.
Both managers will feel frustrated at different periods of the game - it was Chelsea who ended the half the better side, but they were made to work in the opening moments by United.
Cole Palmer had been a standout in the Blues attack, and he won a free-kick early in the second half, as Chelsea hunted for a goal.
Mason Mount had been equally strong, and set up a great chance after some good linkup with Amad down the right - but his finish let him down as it bounced well wide.
United were having a lot of luck down that flank, with Bruno Fernandes often dropping to that side to assist with the buildup. All that was missing was the finishing touch.
Tyrique George looked to have won a penalty for his side after goalkeeper Andre Onana appeared to trip the forward in the box - but a VAR check revealed the ball was won fairly, and the spot kick was chalked away.
Amad Diallo then went down after a challenge in Chelsea's box, but the home side were given the advantage, and Amad was handed a booking for simulation - much to the frustration of the travelling supporters, who felt George should have recieved the same punishment.
With twenty minutes to play, Chelsea had their breakthrough. Reece James spun away from his marker before sending a cross to the back post, where Marc Cucurella was placed perfectly to head the ball home.
There were positive celebrations from the Chelsea players - knowing the goal could be a vital one in their hunt for Europe.
Noni Madueke then should have doubled the lead after being played through one on one, but he fluffed his effort and sent it over the post.
United needed an answer. Diallo had been a standout, especially in the second half, and he produced a powerful near post strike that had to be palmed away by Robert Sanchez.
Amorim had a stronger bench compared to his counterpart - and called for reinforcements, including Alejandro Garnacho and Manuel Ugarte, as his side pushed for an equaliser.
Reece James drummed up the home support as the game entered the final few minutes - with chants of "Reece James, he's one of our own" filling Stamford Bridge.
United were left to defend in added time - youngster Ayden Heaven could have seen red after a high boot lunge on Malo Gusto, but the final decision was yellow.
Not wanting to risk any late errors, Chelsea opted to hold the ball in the corner and run down the clock - arriving at full time with a hard-fought victory.
Chelsea's Player of the Season showcased his skills once again, acting as an effective safety measure to ensure a clean sheet and victory for his side.
Deployed centrally once again in this match, which seems to be his best position, he troubled United's midfielders and prevented Bruno Fernandes from creating goal opportunities.
He attempted thirteen ground duels and won eight - the most of any player in the match - whilst covering tremendous amounts of ground.
These stats have become almost default for Caicedo, who has shone this season under Maresca.