After back-to-back league defeats, City were cruising to victory but Ansu Fati's 73rd-minute reply for Brighton threatened to make it an anxious finale at the Etihad Stadium.
Alvarez opened the scoring in the seventh minute with a scuffed shot following great work by Jeremy Doku.
With influential midfielder Rodri back from suspension, City dominated the first half and Haaland took advantage of some sloppy Brighton play to smash City's second after 19 minutes.
City should have added to their total but Brighton made things interesting when Fati slotted home and the hosts ended with 10 men after Manuel Akanji was shown a second yellow card deep in stoppage time.
Victory lifted champions City back to the top of the table with 21 points from nine games, although Arsenal could go top with a win at Chelsea in a later kickoff.
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