McMenamin came off the bench and made a big impact grabbing what proved to be the winner with seven minutes to spare at Victoria Park on Saturday.
In an entertaining match, Leigh Griffiths gave Hibs the lead in the sixth minute but Stuart Kettlewell levelled three minutes later.
Iain Vigurs then gave County the lead in the 34th minute before Hibs equalised through James McPake on the stroke of half time.
The match looked to be heading for a draw in an equally entertaining second half but super sub McMenamin popped up with the winner.
In the first real attack, David Wotherspoon cut inside and floated a shot just over Michael Fraser's crossbar.
But the visitors went ahead in the sixth minute when Wotherspoon slipped the ball through to Griffiths who drilled the ball past Fraser from 10 yards for his seventh goal of the season..
County got back on level terms three minutes later after they won a corner kick on the left. Richard Brittain swung the ball in and Kettlewell got the final touch to fire high into the net.
There was no let up in the action with play raging from end to end with neither side able to gain the upper hand.
County almost snatched the lead in the 20th minute when Rocco Quinn and Steven Ross combined in the build up and Vigurs drifted a low drive just wide of the far post.
The home side were enjoying a good spell and they went ahead 11 minutes from the break when Vigurs beat Ben Williams to a high ball and he nipped in behind to side foot the ball into the empty net.
But in the last minutes of the first half Hibs hit back. Griffiths curled in a free kick from the left and McPake volleyed home from 12 yards.
Play was more subdued at the start of the second half with chances few and far between at either end.
But Hibs threatened in the 57th minute when a dangerous cross from Ryan McGivern had to be nodded behind for a corner by Grant Munro.
The Edinburgh side were seeing most of the ball without creating too much in the way of goal scoring opportunities.
County were seldom seen as an attacking force and McMenamin replaced Mark Fotheringham in the 66th minute in an attempt to pep up the attack.
But it was Hibs who almost went ahead in the 70th minute when Paul Hanlon let fly from 30 yards but Fraser scrambled across his goal to turn the ball behind.
At the other end, a point blank header from Munro was blocked on the line by McPake as County threatened.
Griffiths came close for Hibs with a rasping shot which clipped off the top of the crossbar on its way over.
The home side pushed forward again and when the ball fell to Mihael Kovacevic who blasted the chance over the crossbar.
The goal was in the balance and it was County who got their noses in front seven minutes from the end when a long ball from Scott Boyd was knocked on by Gary Glen and McMenamin finished close in for his first goal of the season.
County were almost out of sight a couple of minutes later when Vigurs fired a shot off the top of the bar after McMenamin picked him out at the back post.