The stoppage-time victory moved Leeds above Burnley, who beat Millwall 3-1, on goal difference after both sides finished the season on 100 points.
Coventry and Bristol City will contest the play-offs with Sheffield United and Sunderland, while Luton and Plymouth will join Cardiff in League One next season.
Hull narrowly escaped relegation with a 1-1 draw at Portsmouth to finish above Luton on goal difference, who were thrashed 5-3 by West Brom.
Coventry are in the play-offs for the second year in a row after a 2-0 win over promotion rivals Middlesbrough, who dropped to 10th.
Bristol City came from 2-0 down to draw 2-2 at home to Preston to clinch the final spot in the play-offs, but there was heartbreak for Blackburn who agonisingly miss out.
Needing a win at Sheffield United to overtake Bristol City, Blackburn led through Yuki Ohashi but an Anel Ahmedhodzic equaliser nine minutes later consigned them to a 1-1 draw.
Luton suffer back-to-back relegations
After their fairytale rise to the top-flight in 2023, the Hatters have plunged into the third tier in the space of just two seasons.
Tom Fellows and Callum Styles both scored twice for Albion and Daryl Dike also netted as the hosts raced into a 5-1 lead.
Millenic Alli's double and Jordan Clark's goal were rendered irrelevant as Luton faced up to their first season in League One since 2018/19.
The Hatters are the first club since Sunderland in 2018 to drop from the top-flight to League One in consecutive seasons and only the fourth in the Premier League era after Swindon in 1994-95 and Wolves in 2012-13.
Furious Luton fans chanted "you're not fit to wear the shirt" at their crestfallen players after the final whistle.