Second-half goals from Winston Reid, Ricardo Vaz Te and Ravel Morrison allowed the Hammers to climb out of the bottom three with Allardyce putting the return to winning form down to a change of tactics, particularly in attack.
"We thought we would drop the front man out and play more attacking players from midfield, with players from deep running forward," he told Sky Sports.
"The two wide men in Vaz Te and Stewart Downing would run inside, meaning the (Spurs) centre halves would never quite know who they were coming up against.
"In the end, the third goal was an opportunity that showed that and worked really well.
"You try these things, you hope they work, and I said before the game if we got a result it would be great, but if we didn't, I'd probably get slaughtered!
"The players made it work, they have taken it on board and executed it brilliantly. In the end, we deserved what we got.”
Allardyce added: "We got that today, we got three different goals. We had a set-piece, we got a bit of luck and then we had a bit of genius."
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