Everton boss Carlo Ancelotti said 2,000 returning fans made "a total difference" as his side ended Chelsea's 17-game unbeaten run with victory at Goodison Park.
Hosting supporters for the first time this season, Everton's hard-fought win came courtesy of Gylfi Sigurdsson's first-half penalty after Edouard Mendy fouled Dominic Calvert-Lewin.
That woke up Frank Lampard's side who then drew three saves from Jordan Pickford, one of which saw the goalkeeper brilliantly tip Reece James' shot onto the post.
Mason Mount also hit the woodwork for the visitors after 81 minutes, yet they struggled to find the fluidity which has seen them tipped as title challengers this season.