Despite equalising twice through Fredi Kanoute and Trevor Sinclair after a 62nd minute opener from Simon Davies and a penalty from Teddy Sheringham that followed Ian Pearce's sending off for a professional foul on Robbie Keane with just 20 minutes remaining, Glenn Roeder's team somehow left with nothing to show for a courageous and battling performance.
Hammers had been dealt a serious blow after just four minutes of this hard-fought contest, when Tomas Repka was carried off in agony following a 50/50 challenge with Jamie Redknapp that left the Czech defender nursing a badly bruised right knee.
With the visitors temporarily reduced to 10 men, Keane came close to celebrating his Spurs debut with a goal moments later when his acrobatic volley flew just inches over the bar.
Nigel Winterburn then entered the fray in place of Repka, with Dailly reverting to a more familiar central defensive role, and Hammers began to find their composure after a slightly nervy opening.
As he had done against West Brom on Wednesday night, Joe Cole enjoyed a couple of decent chances early on, first firing over from the edge of the penalty area after Kanoute had cleverly stepped over Di Canio's low cross and then curling an effort wide following a superb turn that completely outfoxed Jamie Redknapp.
Yugoslavian midfielder Goran Bunjevcevic was booked in the 28th minute for a late challenge on Steve Lomas who, to his credit, got to his feet immediately and acknowledged that the tackle had been more mistimed than malicious.
On 32 minutes, Spurs suffered their own defensive worries, when Chris Perry was stretchered off with what looked like a similar knee problem to that sustained by Repka. The centre-back was replaced by Republic of Ireland international Gary Doherty.
As the half drew to a close with Hammers looking the stronger of the two sides, Cole and Lomas both saw snapshots fly wide of the target, while Trevor Sinclair fired a low shot just wide of the post following good work from Di Canio and Kanoute.
Tottenham came out for the second period in expectedly more determined mood, switching to a 3-5-2 formation that saw Thatcher replace Taricco, and Ziege curled a free-kick just wide of the post from 25 yards out before Keane fired an effort off target.
Hammers fought back, though, and Kanoute's instinctive header from Di Canio's stinging cross flew just over the bar, while Winterburn got forward to fire in a shot that was deflected away for a corner.
Kanoute then turned provider to send over a cross that Lomas headed just wide, before the French striker was harshly booked for deliberate handball while receiving some particularly close attention from a Spurs defender.
However, just as the Hammers appeared to be gaining the upper hand again, the hosts struck to open the scoring after 61 minutes. Keane's clever pass down the left released Etherington and the young winger cut the ball back into the six-yard box, where Davies got in front of Christian Dailly to guide the ball left-footed under the dive of David James.
It was cruel luck on the Hammers, who had more than matched their north London counterparts for the opening hour but, rather than let their misfortune lead to a capitulation, they hit back - immediately.
Just four minutes after going behind, Glenn Roeder's team levelled. Di Canio's corner was only cleared back to him on the right, and the Italian's deep cross was headed goalwards by Dailly and tapped in at the far post by Fredi Kanoute.
Sadly, the ecstatic Hammers fans weren't celebrating for long. Three minutes later, a chip forward from Bunjevcevic found Keane, who bamboozled Ian Pearce with an outstanding piece of skill that saw him clip the ball over the Hammers defender and skip into the penalty area with only James to beat.
Pearce raced back to redeem himself, but his sliding challenge failed to make contact with the ball and referee Uriah Rennie pointed to the penalty spot before making it a double disaster for the Hammers by showing Pearce the inevitable red card.
Sheringham made no mistake from 12 yards and there seemed to be no way back for the visitors. Once again, though, Roeder's men showed fantastic resilience and character to bounce back and equalise for a second time.
With 13 minutes remaining, Di Canio - who had been about to be replaced by Defoe - was the creator again, clipping in a quick free-kick to the far post, where Sinclair ghosted in to stab the ball past Kasey Keller.
It was no more than the courageous 10 men deserved, and with Michael Carrick - who had been warmly greeted with cries of 'There's only one Michael Carrick' from the Hammers fans as he warmed up - on to shore up things in midfield as a substitute for Di Canio, it appeared we would hold on for a draw.
In fact, had Cole's touch not deserted him at the vital moment as he raced clear from Doherty on the halfway line moments later, things could have been even better.
However, with just two minutes of normal time remaining, disaster struck, and in the cruellest fashion. Young defender Anthony Gardner collected the ball midway in the Hammers' half and fired in a low left-foot shot that seemed harmless enough until it took a wicked deflection off the boot of Gary Breen and spun up and over James into the net as he dived to his right.
Still bottom of the Premiership table and with just one point from the opening five matches, the pressure is certainly mounting for the Hammers, but the reaction at the final whistle from the fans who travelled to White Hart Lane proves that Roeder and his team still have their full support.
The players were clapped from the field as they trudged off disconsolately after a brave display that so nearly produced a memorable and deserving result against high-flying Spurs, and that elusive first victory of the season surely can't be too far away if the Hammers continue to perform in such a manner.