The hosts looked to be heading for victory as they built a two-goal lead, but they needed a penalty from Adam Miller to claim a point after the Shots scored three goals in ten minutes.
Both sides came into the game on poor runs of form and so it looked in a low quality opening.
There was a hint of the madness to come midway through the first half as the game sparked into life with two goals in a minute. Andy Lindegaard nodded Aldershot in front after a slick move, but with the next attack Curtis Weston rifled home a low shot from 15 yards.
Gills surged ahead with two goals soon after the interval. On 49 minutes Mark McCammon, on as a half-time substitute, glanced home Nicky Southall's free-kick for his third goal of the season.
The hosts looked well on their way to victory six minutes later when Andy Barcham sprinted clear to make it 3-1.
Aldershot arrived with the worst away record in the division, but David Winfield gave them hope with a close-range header a minute later. Incredibly they were level just after the hour mark when defender Mark Bentley headed past his own goalkeeper.
Gills were disintegrating and Town, sensing blood, went ahead when Jake Robinson's cross found Andy Sandell completely unmarked to volley home.
With nothing to lose the hosts poured forward and were level again on 71 minutes when Miller won and converted a penalty.
The all-out attacking football continued right up to the final whistle. Barcham missed a glorious chance to win it late on, but in truth neither team deserved to leave with nothing from a scintillating game.