The England international, signed on a season-long deal after falling down the pecking order at Manchester City, demonstrated his ability with a man-of-the-match performance.
Steven Naismith scored the only goal of the game when he headed home from close range in the 45th minute, but Barry's goal-saving tackle to deny Samuel Eto'o earlier in the half was equally crucial.
And Martinez, who was able celebrate his first Premier League victory at the fourth time of asking, told Sky Sports: "That was a master-class.
"You have to remember he has not played competitive football and that shows you how he is as a professional, working hard to keep his fitness up.
"Gareth is quite unique in his profile as a footballer and that is why are so delighted to have him at the club.
"He is a perfect influence for Ross Barkley and James McCarthy, but I though the partnership with Leon Osman was excellent. Gareth Barry was essential in keeping a clean sheet today."
After draws with Norwich, West Brom and Cardiff, Everton secured their first three-point haul of the campaign and inflicted a first defeat of the season on Jose Mourinho's Chelsea.
"It feels really, really good because it was a special game, a special opposition and a very good performance," Martinez said.
"We are still going through a transitional period and I think the crowd understands that and as players we understand that.
"But in the manner that we've been able to defend, sensing danger and coping with one-on-ones then I thought it was superb.
"We always carried a threat and it's not one of those performances where you feel strong defensively but that you don't look like scoring.
"I thought we put a lot of bodies in the box, especially in the first half, even if I thought our build-up play is not as good as it has been.
"But in the second half we kept our composure and always carried a good threat in attack, and we coped with every adjustment that Chelsea did.
"That gives me real pride in the performance."