A goal in either half from Leigh Griffiths gave them a two-goal lead, but the Edinburgh side had to withstand a fightback from Saints, who couldn't add to Steven Thompson's goal.
However, the hosts were perhaps made to rue their penalty miss, with Paul McGowan's first-half spot-kick saved by Hibernian keeper Ben Williams.
But Fenlon thought his side deserved the victory because of their strong first-half performance.
"I was delighted with the performance especially in the first half when we passed the ball well," said the Hibs boss.
"Saints changed their shape in the second half but I then thought we defended well. And at the other end Griffiths and Eoin Doyle are forming a good partnership and always looked a threat."
Hibs have produced two good performances since their opening day 3-0 hammering by Dundee United.
Fenlon added: "Sometimes a manger has to accept the responsibility of the tactics being wrong and I think I got it wrong at Tann...