The Norwegian is back in the City team after a spell on the sidelines with a foot injury, and made the difference as the relegation-threatened visitors made life difficult for last season's treble winners.
Everton manager Sean Dyche was forced to watch from the stands because of a touchline ban and he will have been impressed with their compact and determined first-half display.
However, Dyche would have been less pleased to concede from a set-piece as City made the breakthrough. Everton's players weren't happy with the award of the corner on 71 minutes with them feeling it had been headed behind by Ruben Dias.
And when the cross came back in it was the Portuguese defender who won the first header and the loose ball ricocheted into the path of Haaland who smashed it home from close range.
The goal deflated the visitors and it was 2-0 when Haaland claimed a trademark second. There was nothing intricate about it as he barreled through the middle of the Everton defence and his strength and pace helped him shrug off Jarrad Branthwaite to slot home and make the points safe.
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