Scott Rendell looked to have given United what would have been a terrific three points with his seventh goal in nine games.
But a late goal from David Winfield meant while Jimmy Quinn's side stretched their undefeated start to 12 games, it could eventually prove to be two points dropped later in the season.
To make matters worse for United, on loan Marvin Robinson, on late in the second half, got his marching orders during injury time for two rapid yellow cards.
Robinson, brought in as back-up for United's strikeforce, will miss Saturday's trip to Forest Green as a result of his rash challenges on Winfield and Rhys Day.
Having not let the weight of making history get in their way with Saturday's 2-1 win at Stevenage, Quinn stuck with an unchanged line-up as United sought to knock Aldershot, unbeaten away from home, off their perch at the top.
Quinn's side came out with their tails up with only a strong challenge from Rhys Day preventing Mark Convery from making more of a delightful through ball from Rendell inside the first minute.
John Grant was earmarked as Aldershot's main threat up front and he showed just why as he collected a low ball forward on his toe and continued a powerful run before being thwarted by the cool, calm and collected Mark Peters.
The Shots were getting some joy down the left channel, though, as Anthony Straker fired a vicious long-range drive straight into the hands of Danny Potter.
Ben Harding twice threatened to give Aldershot the advantage as he tried his luck, first with a looping header followed soon after by a 25-yard blast on the volley.
But United's backline held firm despite the visitors' attacking potential by restricting them largely to efforts from outside the box.
Just when Aldershot appeared to be having the better of the play, the in-form Rendell came up trumps on 23 minutes. There was nothing lucky about his seventh goal of the season, though, which he tucked home from close range after a quick but brilliant four-man move that shredded the Shots defence.
United had cause for a penalty appeal soon after when Dan Gleeson appeared to be pushed in the area by Winfield.
But the goal gave United an extra impetus and they began to look a more dangerous proposition going forward.
The never-say-die attitude was summed up by Courtney Pitt's run to stop a ball going out of play just after the half hour. He managed to get the ball back to Stephen Reed, who fired a teasing cross to the far post where Leo Fortune-West was unfortunate to see his header hit the bar and bounce down the wrong side of the line before being cleared.
Rendell then had the time and space to hit a shot from the edge of the box that flew a couple of yards over the bar.
United kept the bit between their teeth and the tempo high after the break with Reed firing just over from 20 yards as the visitors' defence panicked.
And with their direct play stretching the Shots rearguard, it took a fine double save from Nikki Bull to prevent first Rendell and then Pitt from extending United's lead just before the hour.
But United had to stay on their toes against a useful side who have not got where they are in the table by accident.
Mark Albrighton was forced to toe-poke a strike from Straker around the post while Potter clung on to Day's header on the goal-line, unaware play had stopped because of a foul on Peters.
Rendell came off on 79 minutes to a standing ovation and was replaced by new man Robinson in an attempt to add fresh legs to United's cause.
But the Shots finally broke through with two minutes to go,Winfield snatching the equaliser with a header after substitute Joel Grant twisted and turned his way into sending over a cross.
Robinson, though, will wish he had been allowed to stay on the bench.
He was first booked for a challenge on Winfield moments after the game restarted.
But there was no need for the Oxford striker to then follow it with another reckless tackle on Day in the centre circle.
It gave referee Gary Sutton little choice but to show Robinson another yellow and then the red card.
United held out for the remaining four minutes of injury time with Potter making a good stop to deny Rob Elvins' grabbing a winner for Aldershot in the dying seconds.
Source: http://www.cambridge-news.co.uk/
For the official Shots match report and photos, click on the links below:
Match report: http://www.theshots.co.uk/NewsPage.ink?nid=28984
Match photos: http://www.theshots.co.uk/newspage.ink?nid=28994&type=n