A 2-0 victory over West Brom, thanks to Leon Osman's shot taking a huge deflection off Gareth McAuley in the 18th minute and substitute Victor Anichebe's strike off the post midway through the second half, took the Toffees above near neighbours Liverpool.
The Reds, who Everton will face in an FA Cup semi-final in a fortnight's time, have a chance to claw back the initiative at Newcastle on Sunday but Moyes was happy with the effort from his players to get to a position where they can challenge their local rivals.
"If you said to me at the start of the season we would be in seventh with seven games to go I don't think I would have believed you," said the Scot.
"I am just delighted. If you said to me we would be as close to Liverpool as we were I wouldn't have believed you.
"We have never started the season well but if you finish well it leaves everyone with a good taste in their mouth."