Manchester United still look the title heavyweights, but a weak punch cost them dear at White Hart Lane.
United had been defending diligently a lead seized inevitably by Robin van Persie, resisting Spurs' late storm, until their 'keeper David de Gea made his one mistake, leaving United only five points clear of Manchester City.
Games at this level can be about fine lines, about a 'keeper demonstrating total indomitability under sustained pressure. The dropped points will inevitably raise questions over whether United possess the 'keeper of the requisite character to wrest the title back from City. De Gea showed a frailty at dealing with crosses last season but had improved this term.
Yet deep into injury-time here, the Spaniard's punch was poor when attempting to clear Benoit Assou-Ekotto's cross from the left. De Gea was under pressure from Steven Caulker, but he still failed to impart sufficient power into his fisted clearance.
His manager Alex Ferguson focused his anger on the officials afterwards, claiming (rightly) that Wayne Rooney was denied a penalty when his heels were clipped by Caulker, but Spurs also had grounds for grievances, not least when Scott Parker felt fouled in the box by Shinji Kagawa.
The result was fair. Spurs had pressed and pressed for an equaliser, eventually celebrating as if they had secured the title. Fans hugged each other. Andre Villas-Boas looked in the mood to break the world squat-thrust record. Dempsey's goal meant so much.
It was deserved reward for their effort. They showed real belief, ignoring the absence of Emmanuel Adebayor at the Africa Cup of Nations, Sandro through that terrible cruciate injury while Jan Vertonghen was struggling with sickness, and could make only the bench.
The visitors' dug-out was awash with sleet and frustration. Ferguson's team had defended so determinedly and nimbly late on as Spurs tore into them. Rio Ferdinand slid in to block a Jermain Defoe shot and then pushed his head in the way of a Bale strike, diverting it to safety.
They were defending the points, making another statement of their desire to win a 20th title – until De Gea's weak punch failed to clear the danger.
Until then, it had been one-nil to the former Arsenal player. Van Persie has now scored in his club's last five Premier League games, rivaling his best scoring run (with the Gunners in 2009 and 2011). The Dutchman moves so stealthily that here was an opportunity to discover finally whether he really does not leave footprints in the snow.
The icy conditions had briefly placed the game in doubt, but United made their desire for it to go ahead abundantly clear. They do not want fixture congestion. Even in the snow, the show must go on.
United had actually been slow to find their stride. Lennon was quick to trouble Patrice Evra, even drifting inside after 12 minutes and drawing a low save from De Gea. Spurs' work-rate glistened in the floodlit snowfall. United absorbed the pressure, hitting back to devastating effect after 24 minutes.
Kagawa and Michael Carrick combined in the centre and suddenly red shirts were racing forward. Welbeck glided across from the left, keeping the ball away from the attentive Lennon, before picking out Cleverley on the right. His cross was superb, hoisted to the far post.
Spurs refused to be disheartened. Parker and Mousa Dembele kept pushing them forward. Defoe had a shot saved. Bale, hitherto quiet, then appeared in the centre and let fly with a shot that deviated off Ferdinand. De Gea was diving to his right but somehow managed to re-position his shins to keep out the strike.
Spurs were building. Bale stabbed a left-footed shot over. Dempsey then ran on to Dembele's pass but was denied brilliantly by the legs of De Gea. Parker appealed for a penalty after being brought down by Kagawa.
United were defending well. But then came De Gea's mistake. (© Daily Telegraph, London)