Centres Manu Tuilagi and Joe Marchant scored tries as England led 24-10 early in the second half on the back of their most impressive performance for years.
However, in classic style, Fiji scored two tries in four minutes to change the mood, only for England, thanks to surging runs by outstanding number eight Ben Earl, to regain a lead they held on to in a dramatic finale.
England reached their sixth World Cup semi-final and will go in search of a fifth final appearance when they meet France or South Africa.
"There was obviously a spell where Fiji scored two back-to-back tries, which Fiji can do probably better than anyone else in the world.
For most of the match, a fired-up England were unrecognisable from the team who looked so lacklustre against Samoa last week.
Persons:
Farrell, Captain Owen Farrell, Manu Tuilagi, Joe Marchant, Ben Earl, England, Steve Borthwick, Simon Raiwalui, Marchant, Viliame Mata, Peni Ravai, Vilimoni, Simione, Earl, Vilimoni Botitu, Mitch Phillips, Ed Osmond
Organizations:
Fiji, France, Islanders, Samoa, Twickenham, England, Blacks, Thomson
Locations:
South Africa MARSEILLE, France, England, South Africa, Fiji, Paris