Garry Monk's side can pass their previous best Premier League tally of 47 points if they record a third win in a row against the Toffees at the Liberty Stadium.
In addition, skipper Williams and his team-mates are on course for Swansea's best finish as they lie in eighth, while new marks for clean sheets, goals scored and fewest goals conceded are all within reach.
And the Wales international wants no repeat of the late-stumble of 2013, when a post-Capital One Cup slump saw the Swans take just nine points from their last 11 games, as he eyes a place in Swansea folklore.
He said: "We've had seasons here, and the gaffer was involved when he was a player, where it's dropped off like when we won the cup.
"That season still annoys me because we could have done a lot better that year.
"We want to have the best season we've ever had, people forget there's money in it for the club too so we want to keep pushing.
"We want this season to be recognised as one of the best ever for this club and there are so many points still available.
"Every game counts and we want to finish strongly and take the momentum into next season, which we're doing at the minute.
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Ashley Williams has called for Swansea to make history
"We're winning different ways, showing how far we've come on. We are not just same old Swansea, we have said 'no, forget that' and pressed on."
To achieve his aim Williams and company will need to arrest Everton's recent revival under former Swansea manager Roberto Martinez.
"You would expect Everton to be higher," said Williams. "But Roberto is a good manager, and good managers work it out.
"It's only a matter of time, whether you see that this season or next."
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