The Bluebirds fought valiantly, but they exit the Carabao Cup at the Quarter Final stage.
Brian Barry-Murphy made five changes to the side that beat Doncaster Rovers on Saturday, with Dylan Lawlor, Perry Ng, David Turnbull, Joel Colwill and Callum Robinson all coming into the starting line-up.
The first chance of the match went City’s way, as Cian Ashford held off Jorrel Hato well and released Colwill down the right wing, who found the head of Robinson in the area. However, the forward's header went off target.
Turnbull did have the game’s first effort on target, looking for the far corner with an effort outside the area which was safely caught by Jörgensen, while Isaak Davies also looked to break the deadlock after being played in behind the Chelsea defence, but under pressure from Benoît Badiashille, his chance went wide.
Meanwhile City keeper Nathan Trott had to remain alert as Marc Guiu found space in behind the City defence and looked for the near post, with Trott denying the striker with a smart stop with his feet.
City’s best chance of the half came after 34 minutes, as the hosts worked the ball down the left wing. Davies' cross was deflected, almost creeping into the near post before Jorgensen was on hand to make a smart stop and push behind for a corner.
With the scores level at the break, Chelsea began the second half strongly. After Facundo Buonanotte won the ball on the halfway line, he found the run of substitute Alejandro Garnacho, who drew a smart save from Trott.
The visitors would take the lead before the hour mark through Garnacho, as Buonanotte again intecepted a pass, who quickly found the Argentine on the overlap to put the visitors ahead.
Minutes later Trott kept the deficit to one after making a vital fingertip save, tipping an effort from Buonanotte over the bar.
City remained defiant and found an equaliser with 15 minutes to play. After working the ball well down the right-hand side, Ng swung a cross into the area, where Turnbull timed his run perfectly and executed a brilliant header beyond Jorgensen to level the score.
The hosts nearly took the lead a few minutes later, breaking down the right wing again, with the newly introduced Alex Robertson laying the ball to Ng, who took a shot but was denied by the Chelsea keeper.
Chelsea found the night's decisive third goal moments later, as substitute Pedro Neto shot from the edge of the box, deflecting slightly off Bagan's foot before finding the net.
Turnbull created another chance shortly afterwards as his volley was driven into the ground before bouncing narrowly over the net.
The visitors sealed the game in stoppage time, as Garnacho scored again with a shot hitting the far corner.
City’s next fixture is a return to League One action, facing Lincoln City away from home on Saturday, December 20th at 3pm.
Cardiff City: Trott, Ng (Fish 89’), Lawlor, Chambers, Bagan, Wintle, Turnbull, J. Colwill (Robertson 80’), Ashford, Davies (Willock 56’), Robinson (Salech 56’). Subs not used: Turner, Giles,, Mafico, Donczew, Nyakuhwa.
Chelsea: Jörgensen, Acheampong (Chalobah 85’), Badiashile, Tosin, Hato, Santos, Caicedo ©, George (Garnacho 45’), Buonanotte (Gusto 67’), Gittens (Neto 66’), Guiu (Pedro 45’). Subs not used: Sanchez, James, Fofana, Fernandez.