The Hammers looked to be on course to make it three consecutive wins at White Hart Lane when Senegal duo Cheikhou Kouyate and Diafra Sakho had the visitors 2-0 up going into the final ten minutes.
However, Spurs snatched an unlikely point through Danny Rose's fortuitous looping finish and Harry Kane's 97th-minute equaliser - tapped in after the striker had seen his penalty saved by Adrian.
A pulsating game of 39 efforts on goal saw both teams create chances galore. Early on, Spurs were denied twice, with Adrian saving from Nabil Bentaleb and Kane poking against the post.
However, West Ham got stronger as the half went on and took the lead when Kouyate nodded in Aaron Cresswell's left-wing cross on 22 minutes. Sakho was denied by Hugo Lloris before the same player volleyed in Mark Noble's cross on 62, seemingly putting the Hammers in control.
Enner Valencia was then denied by Lloris and Spurs came roaring back late on. First, Rose's first-time shot bounced over Adrian, then Alex Song was penalised by referee Jonathan Moss and Kane converted after the Spaniard had kept his spot-kick out.
"It is very frustrating and a very lucky Tottenham because I think the first goal was a huge slice of luck from their point of view," the manager commented. "We had them nice and quiet and they weren't causing any real problems, then that goal lifted the crowd because they had a chance. They had a huge slice of fortune because he miss-hit the shot and it has bounced over Adrian's head.
"I thought we were going to see the game out nicely, but we made a dreadful mistake when we put a hand on somebody in the box at that late stage. When you're away from home there is huge pressure on the referee and the player goes down brilliantly and the referee has to make a decision and he gives a penalty.
"It's a soft one, but it's given and a huge slice of luck went Tottenham's way again because it's a brilliant save from Adrian and it fell straight back to Harry Kane, who put it in. It's a real disappointment for us because we were magnificent."
While he was left frustrated by the nature of Tottenham's goals, Big Sam was happier with the way Kouyate and Sakho put their chances away.
But, having missed presentable opportunities to put the game out of Spurs' reach, the manager was ultimately left with just one point instead of three after his team squandered a lead for the fourth time in 2015.
"The header was a classic from Cheikhou and Diafra's finish was very good from a tight angle. You have to say we had chances and could have scored more, but we missed easier chances, including two at 1-0 that would have made it 2-0.
"We should have done enough to see it out at 2-0. It's a big disappointment and it's been our Achilles heel since the turn of the year, getting in front and not closing it out.
"We were in front against West Brom, at Swansea and against Man United, but drew them all 1-1, and now we've drawn this one 2-2."