City conceded an equalizer in the 67th minute after Matheus Nunes raised his arm in the area to block a shot, with James Milner converting the penalty for Brighton.
With City noticeably fading, Brighton created a succession of chances before Gruda converted one.
After opening with a 4-0 win at Wolverhampton, City has lost 2-0 at home to Tottenham and now caved at Amex Stadium.
West Ham eased the pressure on manager Graham Potter with a 3-0 win at Nottingham Forest, secured by late goals by Jarrod Bowen, Lucas Paqueta — from the penalty spot — and Callum Wilson.
West Ham lost its first two games in the league, conceding eight goals in the process, and also was eliminated from the English League Cup in midweek.
Later Sunday, Liverpool hosts Arsenal in a meeting of two likely title contenders, and Crystal Palace visits Aston Villa.
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Steve Douglas is at https://twitter.com/sdouglas80
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AP soccer: https://apnews.com/hub/soccer