The Hammers, without an away win in nine road trips since March, soaked up pressure from Spurs before stunning their hosts with goals from Winston Reid, Ricardo Vaz Te and Ravel Morrison within 13 minutes in the second half at White Hart Lane.
The win moved the Hammers out of the bottom three of the Premier League, to Allardyce's clear delight.
"We thought we would drop the front man out and play more attacking players from midfield, with players from deep running forward," the West Ham manager explained.
"The two wide men in Vaz Te and Stewart Downing would run inside, meaning the 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.
"It was getting a little desperate for us in terms of points on the board. I was not over concerned with the performance of the players, it was just about them getting a little more professional in front of goal.
"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."