William Ryder grabbed two first-half tries while Nasoni Roko and Etonia Naba crossed the line to help Waisale Serevi's side to a 26-7 lead at the break.
Timoteo Iosua and Jerry Meafou scored tries for the Samoans as they threatened to fight back but scores for Semisi Naevo and Lepani Nabuliwaqa took the Fijians to a final score of 38-24.
England suffered an awful second day in San Diego but Scotland recovered from an early defeat to make the Plate final.
Both home nations were in the quarter-finals of the tournament's main Cup competition after finishing second in their pools on Saturday.
However, any hopes of glory were soon dispelled as England - last year's winners - lost 19-7 to New Zealand and the Scots fell 34-0 to Samoa.
England had good early possession in their game but a couple of errors gave New Zealand the opportunity to put them under pressure.
A great tackle by Gloucester winger Rob Thirlby stopped the Kiwis from scoring early on as England showed their strength in defence.
But a tackle on Thirlby meant the England player had to leave the match as the opening four minutes remained scoreless in a tense atmosphere.
Tomasi Cama managed to break free of England's defence to score but New Zealand were not able to convert and the lead was just five points at the break.
Dominic Shabbo replaced Michael Hills at half-time but Steve Yates soon widened the gap for the Kiwis.
England replied with a try set up by a thrilling run from Shabbo and finished off by Harlequins 20-year-old Charlie Amesbury, with Simon Amor adding the conversion.
Cama's second try left the gap too wide for England to breach as their opponents progressed.
New Zealand converted two of their tries, with Lote Raikabula and Nigel Hunt the successful kickers.
England's defeat meant they faced South Africa in the Plate semi-finals, but they fared no better as they crashed 21-14.
Scotland put in a storming display at the same stage to dispatch Australia 17-7 - setting up a Plate final with South Africa.
The Springboks proved too strong, however, as they ran out 28-19 winners.