That makes this current run, stretching back to January, the best in terms of successive home wins by any team in the Premier League era.
City were quick out of the traps when Jeremy Doku burst forward down the left and supplied Alvarez to finish in the seventh minute.
We double our lead in the 19th minute when Erling Haaland picked up a loose ball, drove at the defence and powered a shot before Jason Steele and into the bottom corner.
It wasn't plain sailing however, with Brighton growing into the game and pulling a goal back through Ansu Fati in the second period.
A battling display kept Roberto De Zerbi's team at bay for the rest of the game, even with Manuel Akanji's sending off for two yellow cards deep in added time.
Check out the extended highlights above...