London, England – Manchester United fell two points back of 3 draw.
A Jonny Evans own goal handed Chelsea a 1-0 lead at the break, while the Blues needed just 25 seconds into the second half to grab a second as Juan Mata found the net.
David Luiz scored in the 50th minute to make it 3-0, but United began its comeback in the 58th minute with a successful penalty kick from Wayne Rooney.
Rooney scored again from the spot 10 minutes later and Javier Hernandez completed the improbable comeback with a header seven minutes from time.
Chelsea has now drawn its last three games and sits 14 points back of leaders Manchester City.
The first half was lacking in action in front of goal with the lone incident occurring in the 36th minute.
Chelsea's Daniel Sturridge got into the penalty area on the right and tried to pull the ball back to the front of goal, but it deflected off of United's Evans and rolled across the goal line.
But there was plenty of drama after the break with Chelsea doubling its lead through Mata, who scored on a close-range volley following a cross from Fernando Torres.
Mata's free kick five minutes later was headed home at the near post by Luiz, and it appeared Chelsea was on its way to a big victory.
However, United got back into the match when Sturridge brought down Patrice Evra inside the area, allowing Rooney to beat goalkeeper Petr Cech from the spot.
Branislav Ivanovic gave away a second penalty kick 10 minutes later when he brought down Danny Welbeck, and again Rooney got the better of Cech to make it 3-2.
The comeback was complete in the 83rd minute when a left-wing cross from Ryan Giggs found the head of Hernandez six yards from goal and he redirected it home.
Chelsea then had two good chances in stoppage time to claim the win as Mata's free kick was kept out by a great stop from goalkeeper David De Gea, who also needed to tip a shot from Gary Cahill over the crossbar in the dying moments.
Newcastle 2, Aston Villa 1
Newcastle, England - Papiss Demba Cisse scored the winning goal in his Newcastle debut on Sunday, firing home a left-footed shot from the edge of the area that gave the Magpies a 2-1 win over Aston Villa at Sports Direct Arena.
Demba Ba returned from the African Cup of Nations to put Newcastle in front on the half-hour mark, scoring his 16th goal of the campaign after smashing a loose ball past goalkeeper Shay Given.
Robbie Keane leveled the match for Villa deep into first-half stoppage time by heading home a cross from Charles N'Zogbia, but Cisse stole the headlines in his debut.
The Senegal striker came on for the injured Leon Best in the first half, and he made the most of his first appearance by taking a cross from Jonas Gutierrez down off his chest and sending a well-struck half volley into the upper-left corner of the net.
It was a dream start for Cisse and the goal allowed Newcastle to grab its fourth win in five games, taking the team into fifth place.