The mother of two died last week at the age of 43 following a battle with cancer.
Claire was a senior staff nurse at Bolton Hospice and was a regular at Victory Park to watch her husband play for the Magpies in the early 2000s with daughters Ellie, 17, and Jessica, 16.
Danny Mills played for Chorley from 2000 to 2004 and Claire was proud to see daughter Ellie follow in his footsteps by featuring for the Chorley women's team.
The Mills family live in Horwich and the Magpies paid tribute to Claire before Sunday's play-off game by holding a minute's applause.
Vermiglio's players also wore black armbands and the Mills family watched on as the Magpies clinched a spot in the play-off final.
Josh Wilson's equaliser took the game to extra-time, with Chorley eventually winning 3-1 on penalties.
A hat-trick of saves from goalkeeper Matt Urwin gave Wilson the platform to slot home the winning spot-kick.
The Magpies will now host Spennymoor Town in the final on Sunday (3pm).
Vermiglio was aided by Danny Mills at the start of his own playing career at Victory Park.
He has gone on to guide the Magpies to the brink of history in his role as manager
And Vermiglio dedicated the win, that leaves Chorley n one game away from ending a 29- year absence from the top tier of non-league, to the Mills family.
Speaking about the minute's applause Vermiglio said: "It was emotional, really emotional.
"I know Danny quite well. I came to Victory Park and in effect I was coming in to perhaps take his position.
"He made it really well known that he was here. He stood on my toes and made it really physical.
"I got quite close to him and I always watched him and learned a lot from him in the first few years.
"His wife and his family always came to the games. They were a proper part of our Chorley group.
"Part of my team talk on Sunday was about relationships and I think at Chorley you can feel the relationships around the ground, not just with the players but with everyone else who is involved.
"For his family to still be coming and watching Chorley because he played for them just shows what the club is about.
"It was a privilege to just do something for his family on Sunday. They are going through an unbelievably tough time and if we can just give a little bit of something back to someone who has given a lot for the club, then we are delighted.
"He was at the game on Sunday. I had a chat with him and we'd love to dedicate that win to Danny and his family."
Former midfielder Danny paid a heartfelt tribute to his childhood sweetheart.
He wrote: "Claire was a devoted wife, mother, daughter and friend to many and was loved by everyone she met.
"She passed away peacefully, surrounded by her family and friends, and was cared for wonderfully by her hospice friends and colleagues.
"Although dragged to games by her dad Alan many times, she had happy memories and was delighted to see Ellie play for the women’s team this season, telling Ell she was destined to follow in her dad's footsteps.
"Ellie scored her first goal for the club last Sunday and dedicated it to her mum."