The hosts were rewarded for their early dominance when Leigh Griffiths got between Thomas Rogne and Fraser Forster to score the decisive goal.
And the success could be timely for Hibs as they prepare for another derby clash with Hearts following on from their recent Scottish Cup win over their bitter rivals.
Fenlon said: "That's probably the biggest win since we've been here.
"To beat Celtic is fantastic achievement, after the run they have been on of six or seven wins and after qualifying for the last 16 of the Champions League, it is a big result.
"The win against Hearts a few weeks ago was a massive result and I think the players will take a lot of confidence from this result.
"It will give the players a lift. I think over the last three or four weeks, people have started to doubt us a little bit so we have answered a few critics so we are delighted.
"We scored a very decent goal and probably could have scored again before half-time. It was a great finish. He still had a lot to do when he went round the keeper."