Shaw struck with extra-time looming in the Midlands, sending home keeper Darren Acton the wrong way after Carl Palmer had handled a Tom Kearney corner.
And it sets up a home game against either Burton Albion or Droylsden in the last eight of the competition.
The goal came after a second half of almost non-stop Halifax possession with Chris Wilder's side pinning Borough back in their own half for lengthy spells.
That helped an unchanged Town defence keep a second successive clean sheet for the first time this season.
It also followed a solid first half display when Halifax defended comfortably despite playing into the teeth of a howling wind - a wind that dropped almost the moment the half time whistle sounded.
Shaw almost gave Town the perfect start when he capitalised on a poor header from Mark Noon to retrieve the ball in the Borough box, but the cross was cleared.
And Simon Heslop went on a trademark burst from the middle into the area only to send his well struck shot into the side netting.
The home side had their moments, but Tom Curtis fired wide from Simon Travis's half cleared cross and Palmer's 20 yard effort cleared the bar by some distance.
Shaw had a couple of half chances, narrowly failing to get on the end of a Heslop cross and sending in a weak, off-balance shot from the edge of the area.
But it was Nuneaton who had the clearest opportunity to break the deadlock when Travis crossed from the right for Andy Brown whose downward header was saved comfortably by Adam Legzdins.
Borough's chances after the break were few and far between as they were pushed back deeper and deeper.
And Town had a great chance to go in front just before the hour mark when Anthony Griffith found Heslop who played it through for Andy campbell.
The Halifax substitute carried the ball into the area on the right but pulled his shot across goal and wide.
Seven minutes later Matt Doughty's free kick from the right skimmed off the head of a defender forcing the first of a couple of successive corners which maintained the pressure.
The second of them bobbled inside the Borough area allowing Shaw to fire in a shot which was blocked on the line.
And when the ball rebounded to Doughty he struck an right-foot effort that went wide off the outside of the post.
A couple of home attacks were dealt with calmly by Gareth Davies before Halifax returned to the attack.
Heslop's 20-yarder was saved by Acton who did well to get down to his left and push the ball away. Shaw, following up, had his effort blocked by a defender.
A minute later skipper Kearney was also denied by the keeper as he tried his luck from the edge of the area.
Town continued to look for the goal that would surely win the game and when Davies and Danny Forrest combined on the right it opened up the way for Lewis Killeen to fire in a left foot shot that deflected wide.
Kearney took the corner on the left which struck Palmer on the arm on the edge of the six yard box, referee Scott having no hesitation in pointing to the spot.
And Shaw strode up confidently to dispatch the ball into the back of the net and send the Shaymen through.