Martin Woods looked to have put Town on the way to yet another home win, but The Shots spoiled the party.
The Shaymen should have had the win wrapped up with a bow but didn't thanks to a combination of wasteful finishing and brilliant goalkeeping.
Town's youth team were presented to the crowd before kick-off after their cup win in midweek - let's hope that's not the only silverware at The Shay this season.
This result could make that endeavour more difficult now,
Sam Johnson became the new club's record appearance holder and marked reaching that milestone with a couple of smart first-half saves against the run of play, denying Colin Daniel and Tommy Willard.
The latter save came during a flurry of action just before half-time, with Aldershot keeper Ryan Hall keeping out efforts from substitute Woods, Matty Warburton and Billy Waters.
Aldershot lined up in a 5-4-1 system, designed to frustrate and disrupt The Shaymen, and it worked pretty well.
The visitors were deprived of their dangerman Sinclair Armstrong due to injury, and looked a little lightweight in attack as a result.
The Shots were forced back into their own half for the vast majority of the first-half, and Town became more of a threat as it went on.
Jordan Slew brought a couple of excellent saves from Hall, with Town building some momentum as the first 45 progressed, culminating in that flurry of chances.
Halifax weren't helped by Jack Senior's groin injury, meaning he was replaced in the starting line-up by Javid Swaby-Neavin, or by Kieran Green's injury, which saw Woods brought on.
Kian Spence tried to pick the lock that was the reinforced Aldershot back line with some probing passes, but The Shaymen looked likelier to find success in their short, sharp passing into feet, and through the front-four moving around off their starting positions.
When that happened, chances followed, only for Hall to prove unbeatable.
With Solihull leading against Dagenham, the pressure was on Halifax to match their result and preserve third place.
Halifax continued to completely dominate after the interval, but for all their possession, could only create a shot by Spence that was prodded wide six yards out.
But Town finally got the goal they so deserved for their superiority when Woods' left-foot strike from 25 yards beat Hall, who could only parry it into the roof of the net.
It was still all Halifax after the goal, The Shaymen far more dangerous, showing much more intent and intensity.
Warburton might have calmed the nerves had he not volleyed over when well-placed. So too might Waters had his pass to Slew been better when Town broke from an Aldershot corner.
But Aldershot made Town pay for their profligacy when Ndjoli squeezed the ball past Johnson at his near post, popping the party atmosphere like a pin does a balloon.
Halifax: Johnson, Warren, Debrah, Bird, Swaby-Neavin, Green (Woods 25), Spence, Slew (Stenson 87), Warburton, Gilmour (Dearnley 73), Waters. Subs not used; Benn, Thomas.
Scorer: Woods (59)
Shots on target: 7
Shots off target: 9
Aldershot: Hall, Saunders, Lyons-Foster, Phillips, Kinsella, Sylla, Harris (Watts 65), Willard (Bettamer 76), Berkeley-Agyepong, Daniel (Panayiotou 76), Ndjoli. Subs not used: Lokko, Whittingham.
Scorer: Ndjoli (86)
Shots on target: 5
Shots off target: 2
Referee: Paul Marsden
Attendance: 2,662 (249 away)
Town man of the match: Harvey Gilmour and Pierce Bird deserve a mention, but Jesse Debrah gets it for me for another aggressive, authoritative display at the heart of the defence.