After conceding two early tries against Australia last week, England made no mistake this time with Mickey Higham and Burrow both going over in the opening eight minutes.
Higham, in at hooker for James Roby, dived low and hard to grab the touchdown and five minutes later Keith Senior beat off winger Jason Nightingale and he passed into the supporting Burrow to give him a clear run to the line.
Rob Purdham converted both tries to give England a healthy advantage but the Kiwis hit back on 14 minutes when Paul Sykes missed Jerome Ropati and Vatuvei crashed over in the corner for the first of his tries.
Steve Matai missed the conversion but England got back on track three minutes later when Martin Gleeson, in at stand-off in the absence of the injured Leon Pryce and the rested Danny McGuire, took Burrow's pass from a scrum.
England failed to score in the second half of the game
Again, Purdham added the extras and although Lance Hohaia got the Kiwis back into it with a try, things got better for England when the lively Burrow got his second try thanks to a delightful side-step through the Kiwis defence and the kick by the Harlequins man made it 24-8 after 28 minutes.
Matai needed lengthy treatment on what appeared to be a neck injury but on the resumption, Paul Wellens went close to adding another try before being bundled into touch.
Late in the half Nightingale took Isaac Luke's pass to cross at the corner and Luke added the touchline conversion.
But England's second-half display was well below par as they were held scoreless and it gives coach Tony Smith much to think about with the sides set to meet again in Brisbane next Saturday.
Second half start hurt us - Smith
Only an improbable victory by Papua New Guinea against Australia on Sunday can deny England a semi-final spot.
The Kiwis put England under pressure on the re-start and Vatuvei was left with a clear run to the corner after taking Hohaia's cut-out pass but Luke again missed the conversion.
Paul Sykes struggled in the back line and on 55 minutes he was caught out of position which allowed Vatuvai to complete his hat-trick.
Luke's goal levelled the game and then he edged the Kiwis in front with a controversial penalty after he was fouled by Kevin Sinfield.
The Kiwis then sealed their victory when England failed to clear the danger from Bronson Harrison's offload and Nathan Fein followed up to grab the touchdown.
Jeremy Smith added the conversion before Vatuvei set a new Kiwi record by scoring his fourth try to complete the misery.
England: P Wellens (St Helens); M Calderwood (Wigan), P Sykes (Bradford), K Senior (Leeds), L Smith (Leeds); M Gleeson (Warrington), R Burrow (Leeds); A Morley (Warrington), M Higham (Wigan), J Peacock (Leeds, capt), J Jones-Buchanan (Leeds), G Ellis (Leeds), R Purdham (Harlequins). Replacements: K Sinfield (Leeds), G Hock (Wigan), B Westwood (Warrington), J Langley (Bradford).
New Zealand: L Hohaia (NZ Warriors); J Nightingale (St George Illawarra), S Matai (Manly), J Ropati (NZ Warriors), M Vatuvei (NZ Warriors); B Marshall (Wests Tigers, capt), T Leuluai (Wigan); A Blair (Melbourne), N Fien (NZ Warriors), E Tuimavave (NZ Warriors), S Mannering (NZ Warriors), D Fa'logo(South Sydney), J Smith (Melbourne). Replacements: I Luke (South Sydney), G Eastwood (Brisbane), B Harrison (Wests Tigers), D Kidwell (South Sydney).
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