Nacer Chadli and Danny Rose both beat the offside trap inside seven second-half minutes to thwart a Hull side who had made a good start to the second half and had held their own for the majority of the first.
Spurs will secure a place in the Europa League if they finish with victory against Everton but the loss completes a bad week for the Tigers, who lost midfielder Jake Livermore to a suspension following a positive drugs test.
Hull must beat Manchester United at the KC Stadium in the final round of fixtures and hope Sunderland and Newcastle United – who remain in the mix following a 2-1 loss at QPR – are both beaten. A Newcastle draw could also see them safe but only if the Red Devils are beaten.
At White Hart Lane, Steve Bruce’s side paid the price for their failure to capitalise on their strong periods and in particular the failure of Nikica Jelavic to take the only genuine chance of the first half.
After 18 minutes of even exchanges, a counter-attack saw the ball crossed from the right wing by Ahmed Elmohamady and land at the feet of Jelavic, who struck it first time with his left foot, beating Hugo Lloris with power but not the angle of post and bar.
Tottenham did not enjoy a multitude of chances themselves, instead preferring to keep the ball rather than take risks in attacking situations, although they might have done better had Harry Kane opted to shoot rather than pass when in a good position after 27 minutes.
Hull began the second half well and had forced three corners before Spurs made the breakthrough, Chadli collecting a reverse pass from Erik Lamela and going past Steve Harper with his first touch before depositing the ball in the net with his second in the 54th minute.
There was a vague hint of offside about that goal but no doubts on the second, Ryan Mason clipping a superb pass into the path of Rose, who drove it past Harper with his weaker right foot and in a somewhat scuffed fashion.
The timing of the goals left Hull reeling and they struggled to get a foothold thereafter, Spurs passing the ball around with the assuredness of their cushion.
They will wonder how they did not score when substitute Abel Hernandez twice had efforts blocked by defenders, the second almost on the goal-line, and Dame N’Doye thrashed wide, all in the space of 10 frantic seconds.
But they were not costly misses – that had come earlier in the game, when Jelavic had struck the woodwork with the score at 0-0.
A goal then might have changed the course of the match – and quite possibly have altered the grim destiny which, it now seems, awaits Hull City.
Phil Thompson’s Soccer Saturday verdict
“To win the game against Manchester United you have to score a goal and you wonder how that’s going to happen. They’ve had enough opportunities today. It was against the run of play but when you look through the Spurs side there’s probably more quality.
“They didn’t exactly show a lot of it, Spurs, but you thought with this Hull side everything’s against them. This was desperate for Hull City.”
Tottenham: Lloris (7), Dier (6), Fazio (7), Vertonghen (6), Rose (8), Mason (7), Bentaleb (6), Lamela (7), Eriksen (6), Chadli (7), Kane (6)
Subs: Dembele (6), Stambouli (5), Soldado (5)
Hull City: Harper (6), Chester (6), Dawson (6), McShane (7), Elmohamady (7), Meyler (5), Huddlestone (5), Quinn (6), Brady (7), N’Doye (6), Jelavic (6)
Subs: Hernandez (6), Robertson (6)
Man of the match: Danny Rose