The defeat marked City's second consecutive Premier League loss, following their previous setback against Aston Villa, and increased the pressure on manager Enzo Maresca to find an immediate response.
Ayari scored the decisive goal in the 11th minute after a defensive error from Matheus Nunes. A Brighton cross was not properly dealt with by the City defender, allowing the ball to fall kindly for Ayari, who calmly finished from close range.
City attempted to respond and enjoyed long spells of possession, but struggled to turn their dominance into clear-cut scoring opportunities.
Iliman Ndiaye came close to an equaliser in the first half when his header narrowly missed the target, while Brighton goalkeeper Bart Verbruggen kept the hosts at bay.
The visitors also had opportunities to extend their advantage. Maxim De Cuyper missed a good chance shortly after the restart, firing over the crossbar when presented with an opportunity to score.
City increased their attacking pressure as the second half progressed. Ndiaye struck the crossbar, while Nunes was denied by Verbruggen, who produced an outstanding performance to protect Brighton's lead.
Nico O'Reilly also missed a late opportunity with a header, and Jérémy Doku was denied by the Brighton goalkeeper in stoppage time as the visitors held on for all three points.
Verbruggen inspires Brighton to historic victory
Verbruggen was one of Brighton's standout performers, making seven saves as the visitors resisted City's sustained pressure.
The victory was particularly significant for Brighton, as it represented their first-ever win away to Manchester City at the Etihad Stadium.
It also provided a response to their Carabao Cup elimination against City earlier in the week.
Maresca reacts to another defeat
Speaking after the match, Maresca admitted that his team had created enough opportunities to earn something from the encounter but criticised their inability to convert chances.
The City manager also expressed concern about defensive mistakes, saying his team needed to analyse what had gone wrong and improve.
Brighton manager Fabian Hurzeler praised his players for their defensive discipline, highlighting their determination to remain organised under pressure.
Premier League standings
Despite the defeat, Manchester City remained top of the Premier League table with 21 points from nine matches, level on points with Arsenal but ahead on goal difference at the time of the result.
Brighton moved into third place with 19 points, closing the gap on the leading sides after recording their sixth league victory of the campaign.
What next for Manchester City?
Manchester City will look to put the defeat behind them when they travel to Germany to face RB Leipzig in the UEFA Champions League on Wednesday, 4 November.
They will then return to Premier League action with an away fixture against Nottingham Forest as they seek to get their domestic campaign back on track.
Full-time: Manchester City 0-1 Brighton
Goal:
• Brighton: Yasin Ayari 11'