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.
We were due one says Moyes after Everton's good finish
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 to secure a deserved victory.
Moyes felt his side were well worth the victory, having dominated throughout and been denied what he thought 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.
"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."
The Tottenham manager Andre Villas-Boas, whose side have only kept one clean sheet away from home in the league, 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."
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