We lead 1-0 via Darren Anderton's fourth-minute strike and saw Helder Postiga fail to capitalise on the first half's best two chances.
Arsenal looked disjointed and the Highbury crowd were starting to get restless when Thierry Henry broke the offside trap - he certainly looked offside - Kasey Keller saved but Robert Pires pounced on the loose ball for 1-1 after 68 minutes.
Ten minutes later and Freddie Ljungberg's shot flicked off Stephen Carr and looped over Keller's head for a fortuitous winner.
Caretaker boss David insisted: "I couldn't fault the effort, drive and determination of the side. The result was hard to take.
"We could have had three goals by half-time and I thought their back-four was really rocking.
"We didn't want to play on the back foot and we didn't do that, we tried to go for them.
"Helder Postiga missed a couple of chances, but strikers have to remain optimistic. We weren't a lightweight Tottenham side, we were solid but a bit more creative as well."
David Pleat said he couldn't fault the lads after a luckless reverse in Saturday's derby at Arsenal.