The Merseyside outfit - already certain to finish sixth in the table - will surpass their previous best haul of 65 by a point if they beat Chelsea in their season-closing fixture at Stamford Bridge.
It is something Moyes, overseeing his last Everton match before departing to succeed the retiring Sir Alex Ferguson at Manchester United this summer, is keen to sign off with.
Three days after it was confirmed last week that he will be replacing Ferguson, the 50-year-old saw his side take all three points from his final Goodison Park game as Toffees boss when they defeated West Ham 2-0 on Sunday, a match at which the home supporters gave him a rapturous reception.
Reflecting on that encounter and looking ahead to the Chelsea contest, Moyes - who admits the last week or so has been "tough" for him emotionally - said: "We finished the West Ham game off very well last week.
"That has put us in a league position where we can't go any further up or any further down.
"That is great, but we want to try to get a record points total if we can - that would be our final goal.
"It is a good game to finish off with, and it is not a game where there is nothing there."