The hosts went in front in the 12th minute when loanee Josh Barrett crossed for George Fowler to tap in unmarked at the far post, before Knight-Percival drew level from a Jack Payne corner with just 20 minutes to go.
Torrential rain made conditions difficult for both sides, who will both rue a succession of missed opportunities largely caused by standing water on the pitch.
Bradford twice came close to finding an equaliser midway through the first half, but Will Mannion got down well to save efforts from Eoin Doyle and left-back Connor Wood.
The Bantams, who currently sit bottom in League One and are now without a win in eight matches, were undeterred by the worsening conditions and threatened again down the left flank, but Wood’s deflected shot was tipped over by Mannion.
They again came close to levelling in the 54th minute when forward George Miller latched onto Payne’s well-timed pass, but, despite his shot beating the keeper, the waterlogged surface stopped the ball dead before it could cross the goal line.
Aldershot almost hit straight back after Bradford’s equaliser, but Adam McDonnell put his free-kick over the bar and the game finished level.
Elsewhere, Steven Alzate scored his third goal of the season to fire Swindon to a 2-1 first-round win over non-league York City at the County Ground.
National League York were 14 minutes away from taking their League Two hosts to a replay when Alzate struck.
Swindon took the lead in the 12th minute through teenager Scott Twine’s first goal for his hometown club.
Jermaine McGlashan cut a cross back from the byline and Twine neatly back-heeled the ball off the post and into the net.
York equalised two minutes before half time when David Ferguson scrambled home from six yards.
Elijah Adebayo should have put Swindon back in front in the 68th minute after James Dunne’s pass sent him clear but the striker’s weak shot was saved by York goalkeeper Adam Bartlett
Alzate settled an entertaining tie in Swindon’s favour in the 76th minute with a close-range shot after Keshi Anderson had crossed.