Spurs produced arguably their most disciplined away performance of the season to stay five points clear of the fifth-placed Blues, who now face an uphill battle to qualify for next season's Champions League.
It could have been even worse for Chelsea, with Rafael van der Vaart and Emmanuel Adebayor both missing excellent chances as Tottenham enjoyed the better chances.
The draw extended Spurs' winless run to five matches but this was arguably their most crucial point of their entire season on a ground where they had not tasted victory for more than 22 years.
Roberto Di Matteo's Chelsea rescue act, meanwhile, was suddenly in danger of looking futile, with English football's last remaining European representatives now maybe needing to win the Champions League to qualify for the the competition for a 10th successive season.
They might have been ahead inside five minutes today had Didier Drogba - recalled in place of Fernando Torres - and Frank Lampard not got in each other's way.
Chelsea were marginally the better side but both teams almost seemed too scared to lose, with each goalkeeper a virtual spectator during the opening quarter.
Referee Martin Atkinson waved away muted appeals for a penalty in the 28th minute when Lampard ran into William Gallas' trailing leg after Juan Mata's delightful ball in behind.
Chelsea were starting to make inroads and Kyle Walker was lucky a miscued clearance fell just behind Drogba, who was unable to re-adjust.
But Tottenham were a threat on the break and Adebayor wasted a great chance to cross for Walker after skinning Ramires down the left.
There was a brief hiatus when Drogba went down clutching his left knee in apparent agony but was able to continue after some touchline treatment.
The half looked destined to end goalless when Van der Vaart missed a glorious double-chance in stoppage-time, firing Luka Modric's deflected cross straight at Petr Cech and seeing his rebound effort blocked on the line by Ashley Cole.
The danger was still not cleared and Adebayor nodded over at the third attempt.
There was a more purposeful start to the second half from both sides but Michael Essien overstepped the mark by tripping Modric and was rightly booked.
Drogba then produced some classic centre-forward play to roll Gallas and set up the onrushing Daniel Sturridge for a half-volley the forward screwed well wide.
The Spurs fans were briefly celebrating in the 57th minute when they saw Walker ripple the sidenetting after Gareth Bale jinked past two challenges and found the full-back with a delightful reverse pass.
Adebayor then fell over shaping to hit Bale's cross first time before Di Matteo made his first move, sending on David Luiz at right-back for Jose Bosingwa.
Ramires was furious to be denied a penalty after a coming together with Benoit Assou-Ekotto while challenging for Sturridge's cross.
Assou-Ekotto, Mata and Ramires were then all hurt during a skirmish on the right touchline, which saw the former booked for kicking the latter's foot.
Sandro quickly followed for a clumsy tackle on Essien but Van der Vaart escaped with a lecture after reacting furiously to a free-kick awarded for a foul on the same player.
Another controversial Chelsea free-kick saw them go within a post's width of taking the lead 17 minutes from time, Mata whipping the ball against the upright, with the rebound evading both Drogba and Luiz.
Time was running out for the home side and Di Matteo responded by throwing on Torres for Essien, with Spurs boss Harry Redknapp withdrawing Van der Vaart and Sandro for Louis Saha and Jake Livermore.
That came as Modric stood over a free-kick, which Gallas somehow headed over from six yards.
Drogba then sent a weak effort straight at Brad Friedel before Adebayor missed another gilt-edged chance for the visitors.
The striker beat the offside trap to collect Modric's pass and round Cech but gave Gary Cahill a chance to recover and block his finish behind.
The striker nodded over another rebound after Bale hit the bar with the resultant corner, with Tottenham starting to look the more likely winners.
Lampard stung the palms of Friedel with a dipping volley before Di Matteo played his final card by withdrawing Sturridge for Salomon Kalou but Modric's free-kick almost snatched it for Spurs.