Brighton missed the chance to secure the Championship title as Bristol City won to guarantee survival.
The Seagulls, who are a point clear of Newcastle, now must better the Magpies’ result next Sunday to finish top.
They fell behind when Josh Brownhill powered home a header from Matty Taylor’s cross before the break.
The closest Brighton came to a leveller was a stoppage-time header from Glenn Murray that was straight at Robins’ keeper Frank Fielding.
Brighton have now lost both their games since being promoted to the Premier League on 17 April.
The Seagulls will be crowned champions if they beat mid-table Aston Villa on the last day of the season but anything less could see Newcastle win the title instead if they beat Barnsley at St James’ Park.
Manager Chris Hughton will have been disappointed with the flat performance his side put on in front of a packed Amex Stadium, with Bristol City centre halves Aden Flint and Bailey Wright able to comfortably deal with a series of harmless crosses as the Seagulls looked for a route back into the game.
Victory for Bristol City dispelled their lingering relegation fears and means Lee Johnson’s men have won four of their past five games.
They could and perhaps should have extended the lead given to them by Brownhill’s first goal for the club but Taylor totally miscued from close range.