It was a great result for Craig Brewster's side, who have now won two games away from home in the opening three games of the league.
They weathered an early Dunfermline storm when keeper Mark Brown made a stunning left-handed save from Scott M Thomson's header and somehow Andrius Skerla sent a point-blank header wide of the target.
But Inverness gradually clawed their way into things, and Fox took a short pass from Ian Black to fire in a low right-foot shot from 20 yards.
Dunfermline tried to come back after the break but Inverness were always comfortable in defence as Darren Dodds had an outstanding match.
Consequently Dunfermline were restricted to long-range efforts, and Lee Makel came closest with a thundering 25-yarder that crashed off the bar.
And Makel looked the likeliest to earn Dunfermline an equaliser, but his dipping effort in the dying seconds drifted inches wide of the post.
In many ways the effort that Inverness put into the game made them worthy winners, and they worked incredibly hard for each other as a unit.
Jim Leishman, Dunfermline manager said: "We started well and created a lot of chances but their keeper saved well from Scott Thomson and Skerla missed a great chance.
"But it's about scoring goals, and they scored one more than us and that's why they've got three points.
"You've got to make Inverness come out by scoring against them, but it's all about confidence and finding the right finish and we couldn't do that today. However, I can't criticize my players for commitment and desire."
Craig Brewster, Inverness manager, said: "It was nice to get the goal in the first half and Fox produced a great strike.
"I thought Dunfermline started well and threw in dangerous crosses, but we began to break well and deserved to win the match. They never carved us open, and once we got in front I always thought we'd win.
"We're delighted with our start to the season and particularly the performances which we are producing."