João Palhinha's 43rd-minute goal fired Tottenham to Premier League safety with a 1-0 home win over Everton.
Spurs required a draw or victory to guarantee survival after defeat at Chelsea on Tuesday, ensuring West Ham's result at home to Leeds had no bearing on the north London club's destiny.
Palhinha's scruffy goal two minutes before half time earned Spurs a deserved lead at the break, but a nervy second half followed with news of West Ham goals filtering through.
Late drama at the Tottenham Hotspur Stadium
Everton boss David Moyes shuffled his pack and substitute Tyrique George almost produced a last-gasp leveller, but Antonin Kinsky's flying save in stoppage-time confirmed a first Tottenham home league win since December.
The victory sent West Ham down and helped ensure Tottenham avoided a first relegation in 49 years.
A 2-1 loss at Chelsea on Tuesday had ensured a final-day decider for Spurs fans, who lined the streets in their thousands to welcome the team coach and provided a rapturous reception to greet the players onto the pitch.
Match summary
With injured captain Cristian Romero surprisingly present next to the dugout despite a trip to Argentina this week, Spurs started strongly and after an early Everton corner was navigated, Conor Gallagher fired wide.
Tottenham continued to get joy from set-pieces and after Kevin Danso dragged an effort well off target, Palhinha sliced wide while Everton defender Jake O'Brien was cautioned for pulling back Mathys Tel.
A water break followed with temperatures up to 30 degrees in the capital, before Pedro Porro's successful 50-50 challenge on Kiernan Dewsbury-Hall sparked a cry of noise and another Danso effort caused panic in the Everton penalty area.
Tottenham had pressed and probed without finding the breakthrough, but that changed in the 43rd minute. Tel's dangerous corner found Palhinha, who crashed a header against the post but was quickest to the rebound, with his scuffed effort creeping over the line before Thierno Barry could clear.
The Portuguese midfielder raced off down the touchline before he kicked a bottle up in the air into the crowd to celebrate.
Once play resumed, Jordan Pickford almost spilled a shot by England team-mate Djed Spence into his own net before there were stoppages for treatment on Palhinha and Tel.
News of a breakthrough for West Ham at home to Leeds provided an injection of anxiety and Moyes had already introduced fresh legs in Tyrique George and Harrison Armstrong for Everton.
Another water break followed and Postecoglou made his first roll of the dice with substitute Randal Kolo Muani lifting the ball over from 25 yards straight after his introduction.
Fellow substitute Pape Sarr was cautioned soon after for a dive and Spurs required stand-in captain Micky van de Ven to intercept a dangerous cross by Everton substitute George before nine minutes of stoppage time were added on.
Final moments
There was one big moment left as George cut inside and let fly in the ninth minute of stoppage-time, but Kinsky produced a flying stop to clinch a win which helped ensure Tottenham avoided a first relegation in 49 years.