The home side were heading for defeat when Terrell Forbes tripped winger Zavon Hines and Connell scored from the spot.
Bradford would have been a couple of goals to the good in the first 11 minutes but for Shots `keeper Jamie Young, who made two superb diving saves to deny Hines, before then making an equally good stop to tip a 20-yard shot from skipper Gary Jones over the crossbar four minutes before half-time.
However, the visitors, who have now gone six matches unbeaten, shook the home side by taking the lead against the run of play a minute before the interval.
Bradford defender Rory McArdle was booked for a foul on Aldershot's on-loan striker Paul McCallum and the home defence failed to clear Kieron Cadogan's 25-yard free-kick which flashed into the far corner of the net.
Bradford dominated the second half but were denied by a resolute visiting defence until their last-gasp penalty equaliser.
- Sports & Recreation
- Zavon Hines
- Terrell Forbes