City's Gabriel Jesus had two goals ruled out - for handball and offside - and Pep Guardiola's team struggled to break a stubborn Brighton side down until Aguero fired home a pass from David Silva to open the scoring in the 70th minute.
Five minutes later, Brighton defender Dunk slammed a header into his own net as he tried to clear a cross under pressure from Jesus, with the home side lacking the firepower to mount a comeback in the closing stages.
In the end it turned into a routine win for Spaniard Guardiola, who gave debuts to four of his new signings.
England full back Kyle Walker, who arrived from Tottenham Hotspur for a reported 50 million pounds, was a constant menace on the right flank and was man of the match.
"We needed the win and it was good to get off to a good start, so we are happy," he said.
"I am enjoying working with the club, the lads have been so welcoming and I am enjoying my football. It is better to play with a smile on your face."
LATE BREAKTHROUGH
City's breakthrough came within minutes of Guardiola bringing on Leroy Sane, just one member of a star-studded bench from which Bernardo Silva and Raheem Sterling later emerged.
For Brighton, it was a disappointing top-tier return after 34 years, ironically against the same opponents who they faced in their final game before relegation in 1983.
Despite a wall of noise from the home fans, the Seagulls spent most of the game on the back foot, content to concede possession and setting up a compact defensive unit deep in their own half.
In the end they were undone by their own mistakes, with Dale Stephens caught in possession in the lead-up to Aguero's goal and Dunk's own goal sealing their fate in a game City should have won more comfortably given their 75 percent possession.
"It was always going to be difficult for us to score," said Brighton manager Chris Hughton.
"We have to make sure that come the end of the (transfer) window, we have a squad that can do well enough in this division. We have to win the games that we can do."
(Reporting by Neil Robinson, Addtional reporting by Philip O'Connor; Editing by Ken Ferris)
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