The decisive moment arrived 18 minutes from time when Paterson met Dylan McGowan's cross to head home at the near post.
And while Hearts remain rooted to the base of the Scottish Premiership table with minus 12 points, most of the focus is on visiting manager Fenlon whose team are yet to score a competitive goal this season - four defeats from as many matches in Europe and the SPFL.
After a low-key opening 45 minutes, the match sprung to life with a lively second half.
However, Hibs certainly had their chances and more than held their own under the bright sunshine in the Scottish capital.
Substitute Tom Taiwo should have done better from close range when he scooped the ball wide from Liam Craig's cross.
Six minutes later Paterson broke the deadlock against the run of play, yet there was still time for Rowan Vine to race into the Hearts box only to mishit his effort from what appeared a promising position.
This latest loss means Hibs have now conceded 14 goals in their last five competitive matches, dating back to last season's Scottish Cup final defeat to Celtic.