The Norwegian spent his early years in Yorkshire as his father Alfe Inge played for Leeds, but Haaland showed no mercy as City got their Premier League title challenge back on track.
Pep Guardiola's men moved to within five points of Arsenal at the top of the table as they bounced back from a shock defeat to Brentford before the World Cup.
Haaland nearly made his mark inside 45 seconds as he was denied by a fine save from Illan Meslier when one-on-one.
That set the tone for a first half of frustration for City as a series of glorious chances came and went.
Meslier won another battle with Haaland, while two glaring misses from Jack Grealish left Guardiola with his head in his hands.
However, Leeds crucially failed to hold out until half-time on level terms as the visitors finally made their dominance count in first half stoppage time.
Kevin De Bruyne has quickly got over his World Cup disappointment with Belgium to hit his usual heights for his club.
De Bruyne opened up the Leeds defence for the opener and when Riyad Mahrez's shot was parried by Meslier, Rodri swept the rebound into the net.
Grealish made some amends for his earlier misses by creating the second with a smart interception and unselfish pass for Haaland to roll into an empty net.
The City star acknowledged his Leeds past by refusing to celebrate, but it did not stop him adding a second on the night and his 26th goal this season in just 20 appearances.
Grealish was again the creator with a pull back for Haaland to slot home from the edge of the area.
Leeds remain perilously poised just two points above the relegation zone, but did at least get a goal to show for their efforts when Pascal Struijk headed in from a corner 17 minutes from time.
Haaland did at least spare the home side his fourth Premier League hat-trick with an uncharacteristically weak finish with just Meslier to beat once more.
At the other end Joe Gelhardt's curling effort was inches away from setting up a grandstand finish.
But a two-goal margin of victory was the very least City's display deserved as they leapfrogged Newcastle back into second.
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