Aguero fired home in the 70th minute to give City a deserved lead, before Dunk headed the ball into the wrong net just five minutes later.
Brighton started the game with plenty of passion and momentum as they hosted their first Premier League match. However, City soon started to take control and they had a number of chances inside the first 45 minutes.
Brighton's Dale Stephens headed onto his own post 24 minutes in, before Gabriel Jesus had a goal chalked off for handball.
Jesus then had a glorious chance to score nine minutes from half-time but his header and left-footed drive were not enough and the teams went into the break all square.
The Brazilian then had another goal disallowed when David Silva was flagged offside, before Brighton found their feet.
Shane Duffy and Dunk both went close but City eventually found their way through after Stephens lost possession inside his own half.
Kevin De Bruyne stole the ball before charging forward with the ball finding its way through David Silva to Aguero who slotted home.
The points were wrapped up with 15 minutes remaining when Fernandinho's cross was turned in by Dunk, but Chris Hughton will take some positives from his team's first game in the Premier League.