Haaland scored twice for City in their win against Brentford on Saturday.
And with this new brace, the Norway striker has nine goals to his name after four Premier League games, a first in the history of the English championship.
Among the five major leagues, only Carlos Bianchi had achieved a similar feat.
This came in the 1974-1975 season for the Argentune in the colours of Stade de Reims in France.