Everton repeated their 2-1 success over the Cottagers from March 2002 as they lifted themselves to 40 points in the Barclays Premier League with goals from Seamus Coleman and Louis Saha.
A Clint Dempsey strike prevented the Toffees from cruising to victory at Goodison Park but the hosts held on for a deserved win.
Moyes said: "There was a similarity - we went ahead, they got back and it was a bit tense.
"It is a dangerous result 2-0 - the Premier League is not letting any games be won easily, by any side.
"It was a good victory, we had to grind it out. We are missing a lot of key players. My job is to try to find a way of winning."
Source: PA
Source: PA