Moore swooped for O'Halloran on loan deadline day and, after featuring for 90 minutes in the 1-1 draw with Stevenage last weekend, his class shone through against the League Two Spireites on Saturday.
And Moore, while counting the cost of an injury to his skipper James Wallace early in the first half, could not get enough of O'Halloran, who has signed a deal at Prenton Park until January.
"It was a scrappy old first half and the goal we conceded arose from a catalogue of errors - it was awful," said Moore. "But in the second half we got a bit of tempo going and Michael has made a big difference for us.
"He made a great run to help create our second goal and he didn't stop all day. It was a workmanlike FA Cup tie and we probably just about shaded it. We were holding on a bit at the end and it shouldn't have come to that really. I will watch the third-round draw on the television and it can be so nerve-wracking it's ridiculous."
Moore added: "The injury to James is a bad one for us. It is too early to say what it is but it certainly puts a dampener on the result. Hopefully he will be out for weeks rather than months but we just don't know at the moment."