The dismissals came on the hour mark when former Brentford man Rick Newman, making his Shots debut, clashed with Fleets' Peter Hawkins, for which both were shown straight red cards.
Fleet raced into a 2-0 lead early after the re-start courtesy of a Mark De Bolla first half wonder strike, and Charlie MacDonald's second half penalty. But the determination and the team spirit instilled in Terry Brown's men enabled the Shots to emerge with all three points, with a double strike from John Grant on his debut and substitute Ryan Scott's 90th minute winner.
The Shots were quick out of the blocks and it is no exaggeration to say that they should have been at least three goals to the good in the opening quarter of an hour. However Gravesend keeper Lance Cronin, on his debut, was in inspired form making some fine early saves from Mark Pritchard in particular.
Pritchard will feel he should have done better in the sixth minute, when after combining well with Louis Soares, he was thwarted by a fine Cronin save.
Five minutes later, Cronin was again Fleet's saviour. John Grant placed a delicate pass into the path of Pritchard, and with only Cronin to beat, the Fleet keeper snuffed out the danger with another good save.
Aldershot were in dominant mood and should have opened the scoring on 14 minutes.
The alert Darren Barnard took a quick free kick to release the pacy Ryan Williams on the left. Williams pin-point cross found Pritchard in the area, but once again Cronin was able to get down well and deflect his shot for a corner.
Aldershot just could not find an avenue past the inspired Cronin, and when Dean Smith was fouled midway in the Fleet half, Aldershot were given the advantage as Pritchard picked out the run of Soares. The former Barnet man was one on one with Cronin, whose excellent low save foiled the Shots once again.
Fleet had shown some early menace after a couple of early corners, but were largely kept at bay by an excellent Shots rearguard. Midway through the first half, Danny Ekoku linked up well with MacDonald on the edge of the Shots area, but the latter's effort on goal was well stopped by Shots keeper Nikki Bull.
The complexion of the game all changed in the 25 minute, when against the run of play, Gravesend took the lead. Bull had just kept out a fierce MacDonald drive, but Fleet were able to keep up the pressure, as Sasha Opinel took a quick throw in, and finding Mark De Bolla 25 yards out.
The unmarked Fleet debutant took one look up, before unleashing a powerful drive which lodged neatly into the top right-hand corner of Bull's net. The goal wildly celebrated by the Fleet players, however, was met with near silence from the majority inside the Recreation ground.
Three minutes after the re-start, Fleet doubled their advantage. MacDonald, chasing a long ball out of defence, was brought down in the area by Shots last defender Rhys Day. The resultant penalty was precisely despatched low down to Bull's left by MacDonald to send the visitors into dreamland.
But Shots' never-say-die attitude was rewarded on 53 minutes. Soares cross from the right was headed on to Cronin's upright, but the former Halifax man was alert to the rebound to halve the Fleet advantage.
Buoyed on by the crowd, Aldershot drew level through Grant's second of the afternoon on 62 minutes. Once again, Fleet did not deal with Soares' right-sided danger. Pritchard's bravery in the build up allowed an alert Grant to hit the leveller.
A draw would have been a fair result, but substitute Scott pounced late on to deliver the Shots killer blow from Smith's pass.