England will play defending champions South Africa,who beat France by one point in the day’s later clash,in the semi-finals next weekend.
But the Pacific island nation couldn’t complete the comeback in their bid to become the first tier-two team to get to the semi-finals since the game went professional after the 1995 World Cup.
Farrell kicked 20 points for England to guide them to a gripping victory,the result up in the air until well after the allocated 80 minutes as Fiji pushed for a winning try.
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Centres Manu Tuilagi and Joe Marchant scored tries for England and Farrell was unerring with the boot,including the late drop-goal,as England led 21-10 at halftime and looked in total control of the game for the first 60 minutes before holding off a stern Fijian challenge in the final quarter.
Fiji scored tries through number eight Viliame Mata,prop Peni Ravai and flyhalf Vilimoni Botitu,and will rue three relatively simple shots at goal that were missed,as well as unforced errors that eased the pressure on England.
England’s players were largely written off six weeks ago after losing to Fiji – for the first time – at Twickenham in a World Cup warm-up match.