Marco Silva's side knew only a victory would give them a realistic chance of staying up, but goals from Wilfried Zaha, Christian Benteke, Luka Milivojevic and Patrick van Aanholt consigned them to the drop.
Third-bottom Hull, winners just once in their last six matches, return to the Championship just 12 months after their promotion via the play-offs.
They paid the price for a chaotic campaign marred by poor signings and boardroom turmoil.
"The season has been a long, hard slog and it's a sad day. We just came up short," Hull captain Michael Dawson said.
"We were chasing the game all afternoon. The boys in the dressing room and the staff are very disappointed."
Palace had needed a point to stay up and their dominant display completed boss Sam Allardyce's latest survival mission after he rescued Sunderland last season.
Swansea City's win at Sunderland on Saturday had left Hull with no margin for error and Palace's desire to secure their safety meant the stakes couldn't have been higher.
In the circumstances, the first goal would be crucial and Hull, who had won only once at Palace in 32 years, were getting a sinking feeling in south London once again after Zaha punished a terrible blunder to open the scoring in the third minute.
When a Palace pass went astray, Andrea Ranocchia had the simple task of hoofing clear, but instead the Hull defender completely missed his kick and Zaha gleefully pounced on the loose ball to slot home.
With just one away league win all season, the odds were heavily stacked against Hull and Alfred N'Diaye couldn't find a cure for their travel sickness as he blazed well over.
When Puncheon escaped without conceding a penalty after blocking Kamil Grosicki's free-kick with his hand, Silva and his players must have realised there would be no great escape.
Silva sent on Shaun Maloney and Jarrod Bowen at half-time, but Hull lacked poise and Palace held them at bay with ease.
Bowen had Hull's one decent chance to grab a lifeline but he screwed wide from a Sam Clucas cross.
Time was running out for Hull's condemned men and Milivojevic stroked home an 85th-minute penalty after Dawson's foul on Jeffrey Schlupp.
Van Aanholt delivered the final blow with a close-range finish in the 90th minute.