Wrexham remain in third after this defeat but it will come as a big confidence boost for lowly Fylde - watch match highlights here.
It was the Coasters second consecutive win over the Reds after beating them in the FA Cup just over a week ago.
This time goals from Jonny Smith and Jack Muldoon deservedly gave Fylde the points.
“That was our most complete performance of the season by a long shot," said Challinor. "We could have won even more comfortably in the end because we had numerous opportunities. We looked solid in what could have been difficult conditions.
“To beat a team that hasn’t lost for 11 league games, and in the manner which beat them, should fill us with confidence.
“We looked a really good side at either end of the pitch. There could have been a tendency to protect what we had at 1-0 but the lads continued to be positive and deservedly got that second goal.
“We then felt pretty comfortable seeing out the game. We had to deal with some long balls into the box toward the end, but it was our night and we deserved the win.
“We have put in a fantastic display against one of the top sides, so we know we are able of competing with anyone at this level. We now have to show that more consistently.”
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