On 11 minutes Rotherham took the lead with the first serious chance in the game. Reid turned unopposed and hit a full blooded effort from 35 yards.
Mikhael Jaimez-Ruiz - whose goalkeeping fluctuates between the sublime and the ridiculous - lost sight of the ball in the sun, allowing the ball to drop embarrassingly into the net.
Moments later John Grant responded from Scott Davies' corner, but could not keep his headed effort on target.
On 23 minutes, Jaimez-Ruiz went some way to redeeming himself, saving at full stretch with little time to react to Drewe Broughton's header.
Justin Cochrane began to influence proceedings forcing Aldershot into the game. Dean Howell was a hair's width from connecting with Any Sandell's back-post cross.
Howell then delivered a dangerous cross himself, Ian Sharps was first to react, but was mightily relieved to see the ball brush the outside of the post.
In the second half Rotherham were happy containing Aldershot. On the hour mark Andy Warrington was called into action saving well from a close-range Sandell header.
From the subsequent corner Lewis Chalmers headed over a simple chance from five yards.
Seconds later Mark Hudson shot tamely over from the edge of the area, after Anthony Charles misplaced his clearance straight to the striker.
The introduction of Danny Hylton and Kirk Hudson brought some much-needed energy to the home side's attack.
On 65 minutes, Hudson and Hylton combined beautifully from inside their own half.
Hylton picked up the return pass 35 yards from goal, unleashing a piledriver that forced a good save from Warrington.
In the 81st minute, Reid capitalized on a Ricky Newman error, he raced in on goal but overran the ball with Hudson waiting in space.
In the dying moments Anthony Straker crossed to Jake Robinson, the striker's header was well saved by Warrington. Charles reacted quickest to the rebound but was denied by the post.