The Magpies followed it up with Bridget Galloway's dramatic late winner to triumph 2-1 and reach the next stage of the competition.
Those kinds of scenes aren't uncommon for Becky Langley's side this term, and Milne-Redhead believes that the fight shown by United at the Trevor Brown Memorial Ground is testament to the group of players they have assembled.
"We knew it was always going to be a tough game," she told nufc.co.uk. "We weren't going to underestimate them with them being in tier three last season and we knew they were going to be good.
"The game was quite stop-start and it played in their favour but once we went a goal behind we knew that - as we have shown all season - we weren't out of it.
"We know we have goals in us as a team and the win showed the resilience that we have and (our) confidence."
With the Magpies trailing 1-0 with just 15 minutes to play, Langley's team were in desperate need of some inspiration to haul them level.
Milne-Redhead provided it with a rocket from the edge of the box, an area of the game she has been improving on the training pitch.
"Earlier in my career I did start as a number nine and have slowly moved back so that's always an element of my game that I want to use and work on," she said.
"It is something I have been really working on in training. Since we've gone full-time I've had that extra time to be out on the grass and it is an area that I've been working on. It was pleasing for me (to score)."
The midfielder arrived on Tyneside from Coventry United Women in January and after helping United win the FAWNL Division One North title last term, she enjoyed a full pre-season ahead of Newcastle's new campaign in the third tier.
"I think in professionalism it has definitely increased (since going full-time)," she explained.
"The grit and determination is something all the players have always had from last season and before that. I think that is the mentality of the Geordies and the girls that have come in from different regions have adopted that.
"Everyone has reacted really well to (the full-time model) and it's worked really well for us."
Next up for Langley's team is an away trip to Liverpool Feds - the side that pipped Newcastle to the tier-four title two seasons ago.
Regardless of the opponent, the Magpies will underestimate no one, says Milne-Redhead.
"Every single game in the league is going to be a test, there is no denying that," she added. "Ultimately, we are the team that's been promoted. It's going to be a good game and we will have a good week of training and prepare for it in the way that we always do."
Photograph courtesy of Colin Lock
