Having drawn their first two games of the month, the hosts looked as though they may have to settle for a share of the spoils again at Goodison Park when Mauro Zarate's deflected strike cancelled out Romelu Lukaku's opener.
However, Leon Osman secured all three points with his first Premier League goal of the season, leaving his manager delighted.
"I think it is the most satisfying win we've had this season," the Spaniard said. "You know you've been in a game. It's one of those wins where you get that character and winning personality of the squad.
"That's what gives me incredible satisfaction.
"I couldn't be happier with the concentration that we showed, and the way we coped with the disappointment of conceding in such an unfortunate action."
Martinez reserved special praise for Osman, who capped his 400th Everton appearance with the match-winning strike in the 72nd minute.
"I thought he was outstanding throughout the game," he added. "Not just because of the goal, but if you look at his role it was marshalling the back four, dictating the play and playing in quite a deep role.
"So the last thing you expect to see in a counter attack is Leon Osman, [but] he gets into the six-yard box, and he gets the winning goal in a fitting performance.
"He's an incredible ambassador for our football club."
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