The Seagulls - appearing in the semis for only the second time in their history and the first since 1983 - contained the English champions for long spells but ultimately could not recover from Gabriel Jesus's early opener.
City were dominant in possession but far short of their usual best as they edged into a first FA Cup final since 2013, taking another significant step towards an unprecedented quadruple.
Pep Guardiola welcomed back some big guns such as Raheem Sterling, Bernardo Silva and David Silva to his lineup, while fit-again Benjamin Mendy was also handed his first start since November at left-back.
One notable absentee from the matchday squad was Sergio Aguero, but his replacement got City off to a perfect start with the opening goal after less than four minutes.
Aymeric Laporte and Kyle Walker were both involved in the buildup, but it was Kevin De Bruyne who provided the moment of real quality by whipping an undefendable cross into the box which Jesus stooped to nod home from close range.
Brighton's noisy travelling support may have been fearing the worst at that stage as Man City made a trademark quick start to the match, enjoying more than 80% possession during the first 10 minutes.
The Seagulls did slowly begin to grow into the game and stem the tide of City attacks, although going forward they failed to test Ederson with Davy Propper and Anthony Knockaert both firing off target.
Albion's cause could have been aided shortly after the half-hour mark when Walker went head to head with Alireza Jahanbakhsh after feeling that he had been stamped on, and then made a definite forward movement into the Brighton man.
Referee Anthony Taylor deemed a yellow card enough, and VAR backed him up despite the level of ambiguity surrounding the decision.
Walker - who had also picked up a slight injury during the first half - was replaced by Danilo at half time, but he too picked up a booking within five minutes and Brighton made the brighter start to the half.
It took a last-ditch clearance from Laporte to deny a certain equaliser when Shane Duffy rose highest to meet a corner and knock it down into the six-yard box, where Glenn Murray would have hooked it home had Laporte not somehow sliced it over his own crossbar.
Brighton's best moment of the closing stages came four minutes from time when Propper's incisive pass found Jose Izquierdo, who cut inside before firing a well-struck shot towards goal which Ederson plucked out of the air.
It was the only save Ederson had to make, though, and Brighton may feel as though they missed an opportunity to put more pressure on a below-par City side as the game petered out.
Man City were the team that came closest to adding a second goal late on when first Danilo fired over from range, and then Sterling drew a late save from Ryan at the end of a blistering counter-attack which saw Jesus clip the ball into his path.
Ultimately the early goal was enough to send Man City into the final, though, and they will return to Wembley again next month against either Watford or Wolverhampton Wanderers hoping to lift the trophy for the first time since 2011.
MAN CITY (4-3-3): Ederson; Walker (Danilo 46'), Otamendi, Laporte, Mendy (Stones 79'); De Bruyne (Fernandinho 65'), Gundogan, D Silva; Bernardo, Jesus, Sterling
BRIGHTON (4-3-3): Ryan; Montoya, Duffy, Dunk, Bernardo; Propper, Stephens, Bissouma (Locadia 82'); Knockaert, Murray (Andone 66'), Jahanbakhsh (Izquierdo 70')