Leeds needed an Ipswich defeat coupled with victory over Southampton to leap into the top two.
But Daniel Farke’s men lost 2-1 to Saints at Elland Road, meaning he will come up against old club Norwich in the playoff semi-finals.
Ipswich’s most famous fan Ed Sheeran, who sponsors the club’s shirts, was not in attendance for wild scenes of celebration at Portman Road as fans poured on to the pitch and lit blue flares at full-time.
The Suffolk club, which was sold to American investors for just £40 million ($50 million), will now pocket at least £200 million in television revenue in the coming years.
Huddersfield had already been realistically relegated prior to Saturday due to their vastly inferior goal difference compared to their rivals at the bottom.
Burns settled any nerves among the home support when he fired low into the bottom corner on 27 minutes.
On-loan Chelsea winger Hutchinson has been one of the stars of Ipswich’s season and made sure Kieran McKenna’s men could relax by smashing home a second just three minutes into the second half.
Ipswich could face a fight just to hold on to the highly-rated McKenna, a former first team coach at Manchester United.
The 37-year-old Northern Irishman has been linked with a move to Brighton should Roberto De Zerbi leave the Seagulls.
West Brom beat Preston 3-0 to secure their playoff place and will face Southampton.
There was also drama at the bottom of the table as Birmingham were relegated in their first season with NFL legend Tom Brady as a minority owner of the club.
A 1-0 win over Norwich was not enough to save the Blues.
Blackburn spoiled Leicester’s title party with a 2-0 win at the King Power to survive and deny the Foxes amassing 100 points.
Plymouth ended Hull’s playoff hopes with a 1-0 win to hold off Birmingham by a point.
© Agence France-Presse
Photo: twitter @brfootball