The Red Dragons made the most of Leyton Orient’s slip by taking down another of their title rivals.
The Welsh club climbed above the Ammies into second and to within a win of the leaders with a game in hand.
New boss Barrow knows Boxing Day really doesn’t get much better than that.
“I think it has to go down as our best performance of the season,” he said.
“We have been putting in big performance but we haven’t always had big results. Today we did.
“The game has everything. Salford City are a really good side and they are still a really good side but we played very well.
“We had some players who hit their top form and that was a big thing. We just kept going.
“We told them to take the handbreak off and they certainly did that.”
There’s no rest for Wrexham who face Solihull Moors this Saturday.