Ryan Giggs and David Luiz both scored in the opening 30 minutes before Javier Hernández put the visitors ahead on the stroke of half-time.
Gary Cahill levelled in the second half but United winger Nani scored what appeared to be the winner in the 59th minute.
However, Eden Hazard restored parity from the spot in the 90th minute, with Daniel Sturridge and Ramires both scoring in extra-time before Giggs converted a consolation penalty.
Here is the best of the reaction from the professionals on Twitter.
Red Devils striker Wayne Rooney (@WayneRooney) is delighted to see the visitors take the lead: “Giggggggggggggssssssyyy. Yes!”
West Brom midfielder Steven Reid (@stevenreid12) jokes that it was a great assist by Petr Cech: “Great finish #Giggs .. Thanks for that pass Cech.”
Former England captain Michael Vaughan (@MichaelVaughan) hails the United captain: “Best player in the history of the Premier League… Ryan Giggs. Yes I know it’s a cup game but I thought I would let you all know anyway…”
Former Bradford manager Chris Kamara (@chris_kammy) likes David Luiz’s penalty: “Equalising penalty from David Luiz 1-1!”
United defender Rio Ferdinand (@rioferdy5) is pleased for his Mexican team-mate and the young stars: “Chicharito is in one clinical mood lately! 2-1 HT! Let’s finish them off boys. Young defenders doing well, Anderson and Darren Fletcher too..Moses looking lively!”
Former Celtic striker John Hartson (@JohnHartson10) is also impressed by Hernández: “Hernández what a natural goal scorer this lad is – his first touch was brilliant.. out of his feet and into his path sets it up..!”
Everton legend Peter Reid (@reid6peter) is not impressed by Chelsea’s defending: “Chelsea school boy football, sorry, no school boys wouldn’t play like that!”
Ex-United defender Mikael Silvestre (@IamMSilvestre) likes Nani’s strike to make it 3-2: “Naniiiiiiiiiiiiii #goal!!”
Former Liverpool midfielder Dietmar Hamann (@DietmarHamann) is also impressed: “Great goal by Nani don’t know what Luiz is thinking half the time …doesn’t spot danger!
United legend Gary Neville (@GNev2) explains all the goals in the Capital One Cup: “Teams just go for it nowadays. Defending is harder!”
Crystal Palace defender Peter Ramage (@peterramage83) likes the look of the Red Devils young centre-half pairing: “Been impressed with the two young United centre-halves! Stood up and showed a lot of composure on big stage! Been a great game.”
Southampton hero Matt Le Tissier (@mattletiss7) is ideally placed to judge spot-kicks: “How cool was that penatly by Eden Hazard!!”
Celebrity Arsenal fan Piers Morgan (@piersmorgan) is glad to see extra-time: “Extra-time, great – will knacker United out for Saturday.”
Former Sunderland midfielder Michael Gray (@mickygray33) is wondering if there will be another 12-goal thriller: “What a game this is… Looking forward to another 30 minutes of it… 3-3 – are we on for another 7-5???”
Ex-Aston Villa star Ian Taylor (@IanTaylor7) points out a mistake for Daniel Sturridge’s goal: “Wow. What was Wooton doing??? #CHELSEA 4 #MUFC 3 #CapitalOneCup”
Everton captain Phil Neville (@fizzer18) praises his former team-mate: “Ryan Giggs is a phenomenal football player!!!”
Jordan Stewart (@jordanstewart3) enjoys Hazard’s role in Chelsea’s fifth: “OHHHHHH STOPPPPPP ITTTTTT EDEN HAZZZZZZZZARD!!!!!!#SitYouDownLikeAPetDog”
Arsenal legend Ray Parlour (@RealRomfordPele) has enjoyed the match: “What a game at Stamford Bridge which ended 5-4 to Chelsea. What a couple of blinding nights of football #CapitalOneCup!”
Finally, US Open champion Andy Murray (@andy_murray) is out of the loop: “Been any exciting footy games over the last few days?”
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