Despite the win, Erik ten Hag's side end the campaign eighth - their lowest top-flight finish since 1989-90.
Brighton, meanwhile, failed to give departing boss Roberto de Zerbi the perfect send-off, despite having the better chances and dominating possession.
Adam Webster and Joao Pedro came closest to putting the Seagulls ahead in the first half, but they each lacked the clinical edge to beat Andre Onana.
Brighton were left regretting missed chances when Dalot slotted past Jason Steele in the 73rd minute, before substitute Hojlund sealed the three points two minutes before the end of normal time.
The Seagulls end the season 11th, missing out on the top half by a single point.
Manchester United went into the final day knowing they needed a result better than Newcastle's to guarantee seventh place and European football next season.
But hopes quickly faded as the Magpies went into the half-time break with a 3-0 lead at Brentford.
Newcastle eventually wrapped up a 4-2 win, meaning the Red Devils will have to beat Manchester City in the FA Cup on Saturday if they are to secure a spot in next season's Europa League.
-- Courtesy of BBC Sport