Not even Erling Haaland's 150th goal for the club was enough to stop City from dropping points at home for the second time in as many games.
The result on Wednesday (Thursday AEDT) was the side's third straight draw, with Kaoru Mitoma equalising for Brighton in the second half.
Aston Villa also missed out on the chance to move within three points of first-placed Arsenal after a goalless draw at Crystal Palace, and new Chelsea coach Liam Rosenior watched on from the stands as his team were beaten 2-1 by Fulham.
Manchester United's first game since firing Ruben Amorim on Monday ended in a 2-2 draw at relegation-fighting Burnley.
Antoine Semenyo struck a late winner in Bournemouth's 3-2 victory over Tottenham in what could be his last game before a widely anticipated move to City.
At Brentford, Brazilian striker Igor Thiago scored a double for the home side in their 3-0 win over Sunderland.
In the process of scoring his 15th and 16th goals of the season, Thiago broke the record for most scored by a Brazilian player in a Premier League campaign.
For the second time is as many games City blew a lead at home to ease the pressure on Arsenal at the top of the standings.
After their 1-1 draw against Chelsea on Sunday Pep Guardiola's team were held again, this time by Brighton.
Haaland's 41st-minute penalty put City ahead at halftime. But after Mitoma's equaliser on the hour, Haaland was guilty of wasting a golden chance to score the winner when he shot straight at Brighton goalkeeper Bart Verbruggen late on.
A run of three draws also included a 0-0 with Sunderland on New Year's Day.
Second-placed City are five points behind Arsenal, having played a game more. The gap to the top could be extended to eight points if Arsenal beat Liverpool on Thursday (local time).
Villa are third and level on points with City after a 0-0 draw at Palace - the second time in three games that Unai Emery's team have dropped points.
In other matches, Everton and Wolves fought out a 1-1 draw, and Newcastle scored a thrilling 4-3 win over Leeds thanks to a goal by Harvey Barnes in the 12th minute of stoppage time.