City could be knocked off their perch at the top of the table if Arsenal get at least a point at Liverpool on Sunday.
The defeat was City's first at home by Brighton in the Premier League, and though Enzo Maresca's side managed 21 shots on goal, only six were on target and none managed to beat keeper Bart Verbruggen.
"Unbelievable feeling. We go 1-0 up and then to hang tight, the last 30-40 minutes we completely lost control of the game," Verbruggen told Sky Sports.
"The manager said this morning we have to dig deep and that's what we did. So happy to get over the line and can't wait to celebrate with the boys."
City remained top on 21 points, ahead of Arsenal on goal difference, and Brighton remain third on 19 points after six wins and a draw in their opening nine games.
"(We're) just focusing every day on what's ahead of us and the job we have. We will continue to do that and see where it leaves us at the end of the season," Verbruggen said.
City's star-studded attack struggled, with giant Norwegian striker Erling Haaland looking a shadow of himself as his run of scoring in seven successive Premier League games ended.
"We created a lot of chances, disappointing to lose. Didn't manage to put chances away, on another day we put three or four away," City midfielder Elliot Anderson said.
"We're all disappointed. Not good enough, we don't want to be losing games but we've got to stick together - we've had a great start to the season, two disappointing results now, but we have to stick together."