Two goals from Dominic Calvert-Lewin after Richarlison's early opener justified Ferguson's decision to shake up the side with an aggressive 4-4-2 formation as the former Everton striker replaced the sacked Marco Silva in the dugout.
The Toffees doubled their lead through Dominic Calvert-Lewin four minutes into the second half, but Chelsea were quick to respond as Mateo Kovacic netted a precise volley three minutes later to bring the visitors back into the game.
Ferguson's reign got off to the flawless start with Brazil forward Richarlison heading home Djibril Sidibe's cross from the right to give the hosts a fifth-minute lead.
Everton conceded five league goals against Liverpool for the first time since 1982, and the Portuguese coach conceded his players had buckled under the pressure at Anfield. Everton conceded four goals in the first half and could easily have lost by a heavier margin despite Liverpool fielding a weakened lineup.
"Honestly, I won't be going asking for the job", Ferguson said.
Substitutes: Davies (6), Baines (6), Bernard (N/A).
Silva has also been manager of Hull and Watford in the Premier League.
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The 22-year-old was a handful for Chelsea's centre-backs throughout the match and did brilliantly to free up space for the likes of Richarlison, Alex Iwobi and Theo Walcott to cause problems in the final third.
Chelsea FC will now dust themselves down as they look to return to winning ways when they host Lille in the Champions League at Stamford Bridge on Tuesday night.
The result saw Everton provisionally move up to 14th place with 17 points, two points above the drop zone, while Frank Lampard's Chelsea side remain fourth on 29 points from 16 games.
They needed some time to grow into the match and gradually started to look more unsafe on the counter-attack as the clock ticked on, but it was still Everton who were dominating the pace of the match - even when they were out of possession thanks to their pressing.
British media reported that former Everton boss David Moyes is favourite to replace Silva at Goodison Park, although that would likely receive a mixed reaction from the fans.
Starting XI: Kepa (6); James (6), Christensen (6), Zouma (5), Azpilicueta (5); Kante (6), Kovacic (9*), Willian (5), Mount (7), Pulisic (7); Abraham (6). Callum Hudson-Odoi and Michy Batshuayi are the attacking options the Blues have on the bench. "It is about the players and the result and we got it". That's the big thing, body language, getting the fans onside.