Trailing to Clint Dempsey's deflected shot on 76 minutes, Steven Pienaar and Nikica Jelavic scored within 88 seconds of each other in added time to stun their north London visitors.
Manager Moyes said: "It is as good a finish as we've had. We've had a few like that where we've lost and felt low so we were due one.
"I remember a season where we used to score late goals and win games 1-0 but recently it has not been the case.
"If Everton hadn't won we'd have been saying 'How not?' We played terrifically well, especially in the first half with Kevin Mirallas and Seamus Coleman.
"We just couldn't find the final pass or touch to finish it off and Tottenham got better in the 15 minutes after half-time.
"Our poorest period was in the last 10 minutes when we were changing players around.
"We had tried everything to get an opening but they kept at it and we got it in the end.
"It shows the belief and persistence in keeping going and the players showed great character to keep going.
"I thought we had another difficult day (with the officials) with hardly a thing going for us, not a thing and you can't rely on referee decisions going your way.
"We've not had any games where the referee has changed the game in Everton's favour."