Since then they have played 17 matches, winning 12 and drawing five, helping them to a sixth-placed finish last season and leaving them currently riding high in fourth.
To complete the 2013 sweep they need to avoid defeat against Sunderland on Dec. 26 and Southampton three days later.
Those bald figures might suggest that team have carried on seamlessly this season from where they left off in May, but the reality is starkly different.
Despite the impressive nature of their home form, the most progress can be seen on their travels. Moyes had a lamentable away record against the league's big guns but Martinez has already overseen a first club victory at Manchester United in 21 years and an impressive draw at Arsenal where they matched the league leaders pass for pass.
They have lost only one game all season, at Manchester City, and the fans are loving the way he has given his team licence to try to win with style rather than hang on and hope.
His approach will not have come as a complete surprise to the Goodison faithful, however, whose home comforts were rudely punctured in March when Martinez's Wigan Athletic team tore them apart in a shock 3-0 FA Cup quarter-final victory.
James McCarthy, one of Wigan's key players that day and in their run to the Wembley victory over Man City, followed Martinez the few miles westward in the close season but the most impressive thing about his period in charge is that he is achieving success with pretty much the same squad.
True, the presence of on-loan Chelsea striker Romelu Lukaku up front has given Everton a cutting edge that has been sorely missing since Nikica Jelavic lost his touch, and fellow loanees Gareth Barry and Gerard Deulofeu have added stability and zest respectively.
But the likes of Leon Osman, Steven Pienaar, Kevin Mirallas, Bryan Oviedo and Seamus Coleman have really stepped up to the plate and are displaying a confidence born from knowing the manager has given them freedom to try things.
Likewise, centre backs Phil Jagielka and Sylvain Distin, while still a rock solid defensive partnership, have bought into the Martinez way and look to build from the back with short passes rather than their more traditional, low-risk, long-ball approach of recent years.
"It's based on possession, a lot of passing, which starts from the back," said Distin.
"Even last season we played a lot of good football but now it's just constant."
The most exciting aspect of Everton's progress is the emergence of Ross Barkley, a "diamond of English football" to Martinez, into a classy midfielder of the highest calibre.
Still only 20, Barkley has blossomed this season, also breaking into the England team, and is revelling in being the "main man".
It is a situation that makes Everton's decision to allow Marouane Fellaini to follow Moyes to Man United for 27.5 million pounds ($44.98 million) look very good business.
Martinez appears to be handling Barkley perfectly. He rests him when he needs to and does not shy away from reminding him of his weaknesses - notably in his decision-making.
But he knows he has a potential superstar on his hands.
"In Ross, we have someone who, if we look after him properly, can give us something unique," Martinez said after Barkley's stellar performance against Arsenal earlier this month.
"He is someone that you can compare to any other nation...I mean the young Brazilians, Dutch and Spanish players. He has a gift and that talent.
"I've never seen an English player with that sort of mentality and I have had the privilege to work with many youngsters who have been successful. We have to recognise a real English diamond. He isn't ready yet but he has everything to mark a real era in our football."
For Everton, whose last great era in the mid-1980s is becoming a too-distant memory for fans, the combination of Barkley and Martinez and a restored "fortress Goodison" mentality means that they can really start to believe that the next one might be just around the corner. ($1 = 0.6114 British pounds)
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- David Moyes