Trailing to Clint Dempsey's deflected shot 14 minutes from the end, Steven Pienaar and Nikica Jelavic scored within 88 seconds of each other in the 90th minute and added time respectively to secure a deserved victory.
Moyes felt his side were well worth the victory, having dominated throughout and been denied what he though was a penalty for handball late in the first half.
"It is as good a finish as we've had," Moyes said. "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?' because 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, but I thought we had grown into it again when they scored.
"Our poorest period was in the last 10 minutes when we were changing players around and we had tried everything to get an opening, but they kept at it and we got it in the end.
"It can lift you, 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. So you have to win the games, 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."
The win, extending Everton's unbeaten Barclays Premier League run at home to 12 matches stretching back to March, lifted the Toffees back into the top four.