Trailing to Clint Dempsey's deflected shot, 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."
Moyes continued: "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."
Tottenham boss Andre Villas-Boas, whose side have only kept one Premier League clean sheet away from home, was left to bemoan more late defensive frailties. Spurs have developed a poor record for conceding late goals - 10 in the last 15 minutes - and that cost them again.
"It was a disappointing result bearing in mind we were leading taking the game into the last minute," he said. "It has been quite an adventure in the Premier League this season; if we count the number of results that have been going for us before the last minutes we would be first.
"There are so many different reasons. It is not really easy to explain because a couple of them come from different situations.
"You kind of knew as soon as the kick-off went for the 1-1 they (Everton) would go and have a go and they certainly did. It is a difficult blow to take."