Haaland bagged his brace on 79 and 90 minutes before Neymar got a consolation from the spot in stoppage time.
It also moved the talismanic 25-year-old level with Lionel Messi and Kylian Mbappe on seven goals in the race for the Golden Boot.
Norway now progress to the quarter-finals where they will face either England, featuring Elliot Anderson, Marc Guéhi, Nico O’Reilly and James Trafford, or hosts Mexico.
Bodø/Glimt midfielder Patrick Berg’s fourth-minute goal for Norway was disallowed for offside early on before Newcastle’s Bruno Guimaraes missed a penalty later in the first half in front of 80,663 at New Jersey Stadium in New York as the five-time winners from 1958, 1962, 1970, 1994 and 2002 looked to make it through.
But it was Stale Solbakken’s side who took control after the break and it was that man Haaland who made the telling contributions.
The hitman stole ahead of Arsenal centre-back Gabriel to meet a cross from Andreas Schjelderup and put his side ahead deep into the second period.
He then essentially sealed progress with a brilliant low strike from outside the box as the clock ticked down to full-time.
Brazil were handed a second penalty in the dying embers which Neymar despatched for Carlo Ancelotti’s team.
But Haaland was celebrating on full-time as he now gets set for the last eight tie on Saturday 11 July at Miami Stadium in Miami Gardens.
Remarkably, prior to this tournament, Norway had never won a World Cup knockout game and this is their first appearance at the World Cup since 1998 so to beat perennial winners, Brazil, is quite the coup.
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