After back-to-back wins over Crystal Palace and Sunderland, Slaven Bilic's side came into the game brimming with confidence and it clearly showed as the players produced another superb display in front of a record League Cup attendance at London Stadium.
Kouyate got the party started when he thumped home a powerful header early in the game and Fernandes doubled the lead early in the second half with a low finish past Asmir Begovic.
Gary Cahill's injury time goal came too late for Chelsea and Slaven Bilic will be thrilled with the players fighting spirit and quality as they made it through to the last eight of the competition.
It was an all-round team display which helped the Hammers secure a memorable victory, starting with Darren Randolph who once again showed why he is rated so highly by everyone at the Club.
The Republic of Ireland keeper made a fine save on eight minutes to deny N'Golo Kante who burst clear into the West Ham box and saw his low shot produce a fine save from the Hammers keeper.
The Hammers made Chelsea pay for their missed opportunity as they opened the scoring on 11 minutes.
Chelsea failed to clear a corner from Dimitri Payet. The ball fell to Mark Noble who played in the perfect cross for Kouyate and he directed an unstoppable powerful header past Asmir Begovic into the corner of the net.
West Ham had strong claims for a penalty turned down on 15 minutes after Aaron Cresswell laid the ball into Payet and he appeared to be brought down inside the area by Kante.
But referee Craig Pawson ignored the strong pleas from the home supporters and waved for play to continue.
Randolph showed his quality once again on 20 minutes when he made a fine save to deny Nathaniel Chalobah's 25-year shot.
The game was flowing from one end to the other and Manuel Lanzini had a golden chance to double the lead on the half hour mark after Michail Antonio turned David Luiz and crossed in for the Argentine midfielder who had the goal at his mercy but he sliced his shot wide of the post.
Pedro Obiang also came close to getting his name on the scoresheet on 43 minutes when he fired a blistering shot from the edge of the box which was superbly saved by Begovic diving low to his right hand side.
The danger signs were still there for the home side and both Michy Batshuayi and Oscar had good chances to pull Chelsea level just before half-time.
But the Hammers came out determined to add a second and got their wish on 48 minutes when Fernandes continued his dream start to life in the first-team as he doubled the lead for the home side.
The Swiss U21 international cut inside and fired a left-foot shot past Begovic into the corner of the net.
The home fans inside London Stadium went crazy and could now sense this was going to be another special evening under the lights.
Skipper Mark Noble could have made it three on 53 minutes when he curled a shot inches past the post.
Chelsea could have found a way back into game on 73 minutes when Chelsea substitute Diego Costa cut the back for Willian, but he fired just wide of the post.
Bilic sent on Andre Ayew in the final stages of the game and the Club record signing almost made an immediate impact on 82 minutes when he was picked out by Payet inside the box and headed the ball just wide of the post.
Cahill bundled the ball over the line and pulled back a consolation goal in injury time, but it was all in vein as the Hammers held on for a memorable victory.
West Ham: Randolph, Kouyate, Reid, Ogbonna, Fernandes (Feghouli 65), Noble, Obiang, Cresswell, Payet, Lanzini (Ayew 77), Antonio (Zaza 80)
Subs not used: Adrian, Nordtveit, Collins, Fletcher
Bookings: Noble, Reid, Kouyate
Chelsea: Begovic, Luiz, Cahill, Terry, Aina (Pedro 67), Kante, Chalobah (Hazard 62), Azpilicueta, Willian, Batshuayi (Costa 54), Oscar
Subs not used: Eduardo, Alonso, Matic, Solanke
Bookings:
Referee: Craig Pawson
Attendance: 45,957