Shane Long's first goal for Hull saw them claim their first point of the year and end Tottenham boss Tim Sherwood's perfect away record in the Barclays Premier League.
The form book pointed decisively to a Spurs win, with Sherwood having won three in a row on the road while Hull were goalless and pointless throughout January.
But recent arrival Long put the Tigers ahead 12 minutes into his home debut having raced onto a clever ball from fellow new boy Nikica Jelavic.
Spurs deserved to go in behind at the break but, after Paulino's powerful 61st-minute strike drew them level, were good value for a share of the spoils.
Hull, meanwhile, will be delighted by the contributions of Â£14million duo Long and Jelavic - the latter just as deserving of a first goal as his partner.
They were a constant threat and never allowed the below-par Michael Dawson or the returning Jan Vertonghen a moment's peace.
The travelling support took the first opportunity to laud one of their former favourites, chanting the name of Hull midfielder Tom Huddlestone, who left White Hart Lane in the summer.
And it was Huddlestone who played a key role in the first chance of the afternoon.
He caught Spurs cold by floating a wide free-kick towards Jelavic at the near post and although the Croatian's contact was not the cleanest, his volley nearly crept under the crossbar.
With both sides lining up 4-4-2 there was a promise of open football and Tottenham delivered by going close from their very next attack.
Roberto Soldado did well to find Emmanuel Adebayor in space at the edge of the area and his crisp first-time effort was well saved by Steve Harper, the veteran standing in for suspended number one Allan McGregor.
After 12 entertaining minutes, the game got the goal it deserved as Long and Jelavic teamed up to lethal effect.
Jelavic played provider, showing good enterprise to hook the ball into space with his back to goal.
Long galloped after it and immediately gained a yard on Vertonghen and the sluggish Dawson.
By the time the Irishman reached Hugo Lloris he had created a one-on-one opportunity and made no mistake from 12 yards.
Spurs were not immediately panicked by the goal and enjoyed plenty of the ball for the next quarter of an hour.
Adebayor, Soldado and Christian Eriksen all featured but Hull defended stoutly to keep them at bay.
Curtis Davies, in particular, was turning in a fine shift.
Spurs, though, had become a touch complacent at the back and needed Kyle Walker to make a clinical sliding challenge when Jelavic swooped on a loose crossfield pass.
The former Everton man again threatened when Dawson's foul on Long gave Hull a free shot on goal in the 39th minute. Having persuaded Huddlestone to give up dead-ball rights, Jelavic curled his effort a yard wide with Lloris rooted.
Spurs continued to struggle against Jelavic after the interval, Walker dithering near the corner flag and complaining to the referee as the Croatian picked his pocket.
By comparison, it was not until the 56th minute that Harper was called on again.
Vertonghen's rampaging run got Spurs going before Paulinho's shot was diverted into Soldado's path. He took aim from a tight angle but Harper kept his cool to palm clear.
The equaliser felt likelier now and arrived just after the hour mark.
A short free-kick resulted in Danny Rose's hopeful shot from 30 yards and while that was never likely to worry Harper, it did reach Paulinho, who turned and found the roof of the net from 18 yards.
Sherwood's side were immediately improved and quickly forced Hull back into their own half.
For a while, they defended desperately but Spurs' new-found confidence invited a quick counter.
Substitute Robert Koren nearly took advantage when his through-ball found Jelavic and, though he managed to stab his shot past the charging Lloris, Dawson was on hand to prevent it reaching the line.
Jelavic, who did everything except score on the day, struck the base of the post after more good link-up play from Long but the feeling remained that Hull were happier with the scoreline.
Had Adebayor had one of his better days, or Eriksen's radar been better adjusted, Spurs would surely have scored again.
Hull might also have nicked it when Huddlestone's flat free-kick in the 89th minute somehow evaded three team-mates inside the six-yard box, but neither side will be aggrieved with a draw.