In their first ever quarter-final, Andreas Schjelderup fired Norway into a shock lead in the searing Miami heat.
But Bellingham, who also netted a double in a memorable 3-2 over Mexico in the last 16, produced a moment of magic to equalise just before half-time.
Norway had a second goal controversially disallowed after a VAR review in the second half for a foul by Erling Haaland as both sets of players were pushed to their physical limits by going to extra-time.
Bellingham came up with another big moment as he pounced on an error by Orjan Nyland to sweep in his sixth goal of the tournament for the winner.
England will face Argentina or Switzerland on Wednesday for the chance to reach a first World Cup final in 60 years.
“We are in the last four. It’s amazing but not happy with the performance, in every sense,” said England boss Thomas Tuchel.
“We made life difficult for (ourselves) in the way we played and how we played — sloppy, a lot of technical mistakes, not fast enough, not repetitive enough. We were lucky today.”
Haaland’s spectacular run of scoring in his last 14 competitive matches for Norway came to an end against the land of his birth with Norway’s exhausted talisman replaced at half-time of extra-time.
Having failed to win a World Cup knockout game after conceding first since the final of 1966 before this tournament, England have now done so twice in three matches.
The 5pm local time kick-off in Florida meant that temperatures remained above 30 degrees Celsius throughout, with intense humidity making for draining conditions for the players.
The heat looked like it would spoil the spectacle as the first quarter was played at a walking pace.
However, it sparked into life after Schjelderup’s effort flew over Jordan Pickford into the top corner.
Norway suddenly had Tuchel’s men rattled and were left to regret not doubling their lead.
Pickford saved low from Martin Odegaard before Alexander Sorloth wasted a glorious chance when he failed to feed Haaland and instead went for goal himself.
Almost immediately Bellingham pulled his team out of the mire once more.
Bellingham had been well marshalled until he collected Anthony Gordon’s pass, burst into the box at speed and then slotted home on his weaker left foot.
Momentum was suddenly in England’s favour and they nearly went into the break ahead.
Bellingham was this time the creator for Kane, who dinked the ball coolly over Nyland, but had just drifted offside.
Tuchel introduced Bukayo Saka and Eberechi Eze at the break for the ineffective Noni Madueke and Declan Rice — the Arsenal midfielder had been suffering with illness earlier in the week.
But those changes left England light in midfield and they were left hanging on at spells in the second half.
Torbjorn Heggem made the most of some sloppy defending to turn in at the back post, but Haaland was penalised for a push on new Manchester City teammate Elliott Anderson before the corner had been taken, and the goal was disallowed.
Norway were inches away from a winner again when Kristoffer Ajer hit the bar after England fail to deal with another dangerous corner.
Both sides visibly wilted in the energy-sapping conditions late on but were forced to endure an extra 30 minutes.
Nyland had been Norway’s supporting act in the last 16 win over Brazil with a series of saves before Haaland struck twice late on for a landmark victory.
This time the Sevilla goalkeeper was the villain as he spilled substitute Morgan Rogers’ shot from distance and Bellingham pounced and scored.
England were awarded a penalty moments later, but this time VAR intervened in Norway’s favour to deem Djed Spence had initiated contact inside the box.
Yet, Norway’s spirit was already crushed, epitomised by a slouched Haaland watching on from the bench with nothing more to give. (AFP)
