Newcastle forged into a 2-0 lead at the interval but a comeback looked on as Erik Lamela fired home on 61 minutes and Aleksandar Mitrovic was sent off for a challenge on Kyle Walker seven minutes later.
However, the Magpies scored next for 3-1 and as we pushed forward, we were cut open on the break and two goals in 60 seconds five minutes from time sealed our fate.
The result sees us finish in third place for the first time in the Premier League era and qualify for the Champions League.
Mauricio Pochettino made just one change to the side that was beaten by Southampton last weekend with Ben Davies coming in at left-back for Danny Rose, who dropped to the bench.
We controlled the opening exchanges with patient build-up play as Harry Kane fired an early warning shot over the bar inside five minutes.
The home side grew into the game, though, and five minutes later Mitrovic went close when he stretched to get on the end of a dangerous cross from Daryl Janmaat.
It was not long before the home side took the lead when Mitrovic laid the ball into the path of Georginio Wijnaldum, who kept his cool to slot home from 12 yards.
We hadn’t been anywhere near our best and things got worse with five minutes of the half remaining as the already relegated Magpies doubled their lead. Moussa Sissoko was the provider this time with a floated cross from the right that was met perfectly by Mitrovic, who thumped a header past Hugo Lloris.
Christian Eriksen finally created our first chance of note in the dying stages of the half when he brought a fine save out of Karl Darlow from a tight angle after Kane had slipped him in.
We made two changes at the break with Josh Onomah and Tom Carroll coming on to replace Ryan Mason and Heung-Min Son.
Eric Dier wanted a penalty 10 minutes into the second period when his shot was charged behind for a corner, but referee Anthony Taylor felt there was no case for handball.
It sparked our best spell of the game as Davies created an opening for Lamela soon afterwards but he failed to get any conviction on his shot and it was easily saved by Darlow.
At last we found a breakthrough just after the hour mark as Lamela pulled a goal back. Eriksen and Dier combined before the latter rolled it into the path of Lamela, who lashed in a shot from a tight angle that Darlow was powerless to keep out.
The intensity returned and Onomah came close to his first Spurs goal on the angle two minutes later and then came another twist in the tale as Mitrovic was sent off for a dangerous tackle on Walker.
Eriksen almost levelled it up with 22 minutes to go with a curling effort from distance that just dropped over the bar.
We were looking more likely to get the next goal but completely out of the blue the home side made it 3-1 from the spot. Sissoko led a breakaway and referee Taylor adjudged that he was fouled under pressure from Jan Vertonghen and Eriksen. Wijnaldum sent Lloris the wrong way, meaning we had a mountain to climb.
Carroll flashed one past the post soon afterwards and Sissoko brought the best out of Lloris as the chances continued to flow with time running out.
Former Spurs man Andros Townsend should have killed the game altogether but scuffed a shot into the arms of Lloris before Sissoko again flashed a shot narrowly wide. Lloris was again to the rescue with eight minutes to go when he once more denied Sissoko with a brilliant one-on-one save.
However, there was no stopping Newcastle youngster Rolando Aarons' shot from the left angle which came shortly after Townsend had hit the post as the home side increased their lead on 85 minutes.
And a minute later it got even worse as Janmaat went through on the break and slotted beyond Lloris.
Kane saw a shot clip the post in stoppage time but ultimately we wound up 2015-16 with our heaviest defeat of the campaign.
Newcastle (4-2-3-1): Darlow; Janmaat, Taylor, Mbemba, Dummett; Colback, Tiote (Shelvey 62), Wijnaldum (Aarons 76), Sissoko (c, Sterry 84), Townsend; Mitrovic. Substitutes (not used): Woodman, Cisse, De Jong, Perez.
Spurs (4-2-3-1): Lloris (c); Walker (Chadli 70), Alderweireld, Vertonghen, Davies; Mason (Carroll 46), Dier; Son (Onomah 46), Eriksen, Lamela; Kane. Substitutes (not used): Vorm, Rose, Wimmer, Clinton.
Goals: Newcastle – Wijnaldum 19, 73 (pen), Mitrovic 39, Aarons 85, Janmaat 86. Spurs – Lamela 61.
Yellow cards: Newcastle - Aarons 86. Spurs – Mason 45+2, Lamela 63.
Red card: Newcastle - Mitrovic 69.
Referee: Anthony Taylor.