Oldham boss Lee Johnson was livid with match official Ilderton, who pointed to the spot when Oldham goalkeeper Mark Oxley dived at the feet of Tranmere substitute Ryan Lowe in the fourth minute of time added on.
Oldham were convinced that Oxley had made clean contact with the ball, but Lowe picked himself up and sent the keeper the wrong way to give Tranmere their first win of the season.
Moore, celebrating a third straight victory against his former club, said: "It's always pleasing to come here and win because they love to hate me and I don't know why.
"This is a massive result for us - it doesn't matter how you get them, as long as you do.
"In the first half our system didn't really work and we couldn't get people on the ball, but after half-time we got forward more
"We got a bit of luck when we needed it, but we also defended well when we had to.
"Oldham had a lot of pressure, but our keeper didn't have to make many saves and we stopped them creating much from set-pieces.
"After an hour I thought it looked a certain draw, but it was a nailed-on penalty at the end.
"Ryan Lowe was on the front foot to get in front of their keeper and, although the referee had to be brave to give it, he didn't have much option."