England dominated the out-of-sorts All Blacks at International Stadium Yokohama on Saturday to set up a showdown with South Africa or Wales at the same venue next weekend.
Tuilagi touched down for a try that Owen Farrell converted inside two minutes and George Ford's penalty just before the break put Eddie Jones's inspired side 10-0 up at half-time.
The defending champion never really got going in an error-strewn display and although Ardie Savea's try gave it hope, another three penalties from the excellent Ford kept England in command.
England, which also had tries from Sam Underhill and Ben Youngs ruled out, was lively in attack and outstanding in defence, sealing a first win over New Zealand for seven years and a maiden Rugby World Cup triumph over the holder to replace it at the top of the world rankings.
New Zealand's first Rugby World Cup loss since 2007 ensured there will be no dream swansong for head coach Steve Hansen, while captain Kieran Read will end his stellar Test career with a third-place play-off.