The goal by Ross Barkley ignited the comeback from Luton which almost saw them come from three goals down to draw.
Sadly for Rob Edwards' side, they just could not find that third goal.
Barkley was integral to everything Luton Town did well today and is starting to shine in the heart of this side.
Luton had their first shot on target in the 77th minute and then in the remaining time they had six shots on target, hit the crossbar twice and had a goal disallowed.
Chelsea can count themselves lucky to hold on for the win in the end.
Rob Edwards' side turned the screw in the final moments and came so close to scoring an equaliser.
The referee brings this titanic battle to an end at Kenilworth Road.
Chelsea hang on for a vital three points.
For Luton, they will feel they could have got something out of this.
90+4. Gusto is shown a yellow card for delaying the throw in for too much time.
Chong turns away from Gallagher and is fouled once again.
Luton are hoping that they can create one more chance now.
90+2. Chelsea have brought Gilchrist on for Cole and switched to five at the back now.
Chong whips another dangerous ball in but Ogbene cannot control it at the back post.
Rob Edwards punches the air in anger that they could not turn it in.
90. Moments ago Chelsea fans were singing about how their team was the best in the world.
It's highly debatable if they are the best team in Kenilworth Road right now.
Chong gets to the byline and whips the ball in and Thiago Silva clears the ball from his own goal line.
We are going to have an additional six minutes added.
88. We have a game on our hands now.
As the cross comes in from Ogbene as it is fired towards goal, Petrovic makes a save but the ball loops up in the air.
Adebayo is on the back post to volley home and send Kenilworth Road into raptures.
86. Gallagher goes into the back of Chong, giving away a foul.
Doughty stands over the free kick.
He finds Morris at the back post and his header comes crashing off the crossbar.
The replay shows that Petrovic got a fingertip to it, great save.
84. Ogbene gets another good delivery into the box.
Chelsea fail to deal with the cross and Doughty keeps it in play.
Morris gets his head to it but Petrovic makes the save.
82. As the corner comes in from Luton, Barkley meets it at the near post with a header to finally put the ball into the back of the net for Rob Edwards' side.
They had their first shot on target in the 77th minute and now they have their goal.
Another one for the hosts would make for an interesting end to this game.
80. What a miss for the hosts.
Ogbene crosses from the right and Adebayo thunders his header against the crossbar from two yards out.
Petrovic didn't move, he had to score.
78. Chelsea fans are starting to enjoy their day out here.
With time running out, you cannot see them losing this now.
Barkley looks to place a shot from outside the box but it is straight at Petrovic.
76. For a moment there, Luton thought they had a chance to get back into this game.
As the replay shows, Adebayo was coming back from on offside position in the build up.
He finished well as the cross came in, heading into the bottom corner, but it was to be ruled out.
74. It seems a bizarre decision by Man City to let Palmer leave.
He has so much to offer and is only going to get better.
The player seems to rarely be injured also, which is key to any side.
72. Palmer has been the difference between these two sides.
The quality and skill of the Chelsea youngster has just been too much for Luton to cope with.
That said, Kabore got the ball rolling when he passed the ball to Palmer to gift him his first goal.
70. That is surely game over now.
Palmer makes a run and is slotted in, he skips around Kaminski and dummies a shot so the defender commits himself.
He uses that to slide the ball into an empty net.
68. Madueke plays a short corner to Palmer.
He checks onto his left and looks to fire a shot away.
Chong does well to block and bring the ball out for Luton.
66. Jackson is being booed whenever he receives the ball.
A challenge comes in on him again and he is rolling around on the floor.
'You are embarrassing' rings out from the home fans.
64. Morris has been brought on as Luton try to create something.
Chong is causing problems for Chelsea, he is covering a lot of ground.
The visitors try to press high up the pitch but Kaminski is happy to go long with a pass.