Farrell kicks England to narrow quarter-final win over fighting Fijians
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.
"For large parts of the game we controlled it," said England coach Steve Borthwick.
"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.
"What we needed to do then was stay composed and find a way to get back ahead on the scoreboard and that's what the players did."
At the same ground 16 years ago Fiji had a similar experience, fighting back to go level with South Africa in the quarter-final and they again fell just short of becoming the first Tier Two team to reach the semis.
Emotional coach Simon Raiwalui took a positive view, however.
"This is a different Fiji team and I think it’s the start of something special," he said.
"We made a couple of mistakes today, we didn’t take our chances and we paid for it, but I couldn’t be prouder."
For most of the match, a fired-up England were unrecognisable from the team who looked so lacklustre against Samoa last week.
They blasted out of the blocks and Tuilagi showed great dexterity to spin and reach back to touch down for the first try. Another slick break set up Marchant, who used sharp footwork and a telescopic arm to claim the second.
FIJIAN FIGHTBACK
However, down to 14 with winger Vinaya Habosi in the sin-bin, Fiji hit back as Vilimoni Botitu flipped a pass backwards through his legs for Viliame Mata to score under the posts.
It was a rare attack, though, and more England pressure earned penalty opportunities that Farrell gobbled up to build a 21-10 lead half-time lead, which they stretched to 14 points after 55 minutes.
England's fans were planning for Paris but suddenly Fiji struck back with tries by Peni Ravai and Vilimoni Botitu after superb Semi Radradra offloads and with Simione Kuruvoli converting both it was 24-24 10 minutes from time.
To their immense credit, however, England remained calm and surging runs by the irrepressible Earl set up Farrell for a drop goal and a penalty which the fly-half knocked over with three minutes to go.
There was still time for drama, however, as England held off a relentless series of attacks and thought they had won it, only for Farrell to be penalised for a deliberate knock-on before winning the decisive penalty with 86 minutes on the clock.
When England were stunned at Twickenham by Fiji in August it was their fifth defeat in six matches and they set off for France with criticism raining down from every angle.
Now, on the back of five wins in a row, the 2019 World Cup runners-up are in the last four again.
Critics will point to their stuttering performances and relatively easy path but there is no denying that coach Steve Borthwick has plotted a route through the tournament.
England will undoubtedly have to find another level of attack but, on the back of Sunday’s improvement and their superlative display to beat the All Blacks in the semis four years ago, there will be much talk of "anything can happen on the day" during next week’s build-up.