Harry Kane and Pedro Porro scored early in either half to put Spurs 2-0 up and, although Jack Harrison reduced the deficit, Kane struck a game-clinching second in what could be his last game for the London club.
Tottenham substitute Lucas Moura rubbed salt into Leeds’ wounds by waltzing through a porous defence in stoppage time to complete their misery.
Leeds went into the final day needing not only victory, but for relegation rivals Everton and Leicester to drop points and, since they both won, the Yorkshire club’s 21st league defeat of the season was immaterial.
The hosts have not kept a clean sheet since February and their hopes of doing so on Sunday went up in smoke in just the second minute.
The ease with which Porro and Son Heung-min combined to carve open the defence typified Leeds’ season, with Kane finding space among headless chickens to hit the first nail into the home side’s coffin.
Leeds fans responded to Kane’s 28th league goal of the season with raucous defiance, ‘We’re going down’ being one of their chants.
Leeds’ players rallied and did their best to give something back to the Elland Road faithful, but in terms of confidence and quality they have long been running on empty.
Robin Koch spurned their best chance, heading wayward from in front of goal from Rodrigo’s brilliant cross before Pascal Struijk’s shot was deflected for a corner.
Adam Forshaw’s fierce drive was blocked by Davinson Sanchez and another Koch header curled the wrong side of a post.
Leeds boss Sam Allardyce cut a forlorn figure in the dugout and saw his side waste further first-half chances as Rodrigo headed Forshaw’s cross off target and Rasmus Kristensen volleyed over.
Tottenham continually threatened on the break without creating any more first-half scoring chances, but they soon remedied that.
Just as they had done in the first half, Leeds conceded inside the opening two minutes of the second as Kane brilliantly set up Porro, who arrowed a low shot into the far corner from a narrow angle to put the visitors 2-0 up.
Leeds gamely searched for a goal of their own and were rewarded when Harrison made space on the edge of the area to drill a low shot into the far corner.
But within two minutes Tottenham restored their two-goal advantage.
Sanchez’s simple long clearance caught Leeds’ defence all at sea and Kane curled a neat finish inside the far post.
As Leeds fans vented their fury at their club’s plight in the closing stages, Moura – on his last appearance for the north London club – completed the scoring after a mazy run from halfway before chants of ‘Sack the board’ rang out through the home terraces.
Tottenham Hotspur: Forster, Emerson, Sanchez, Lenglet, Davies, Porro (Lucas Moura 90), Bissouma (Craig 77), Skipp (Abbott 90), Son (Richarlison 76), Kulusevski (Sarr 67), Kane. Unused subs: Danjuma, Tanganga, Austin, Alonso.