County should have scored in the opening seconds when Ben Harding failed to clear his lines.
John Thompson picked up the loose ball on the edge of the area and fired low inside the post.
Mikhael Jaimez-Ruiz made an excellent save by pushing the ball onto the post in his second game in league football.
Moments later, Sean Canham defied the laws of physics by shooting over from five yards in front of an open goal after good work down the left flank from Myles Weston.
Unperturbed, Aldershot took the lead through a deflected Harding drive from 18 yards and Josh Lillis' first action in the game was to pick the ball out of the net.
On 18 minutes, Phil Pickens played Hamshaw into the box but Jaimez-Ruiz came out well to smoother the midfielder's effort.
In the closing moments, Scott Davies almost doubled the home side's lead but Lillis got down well to his right to thwart the danger.
At the start of the second half, Canham missed another sitter by hacking wide from three yards after Anthony Charles had sliced the ball to the striker feet.
On 54 minutes, Hamshaw forced another spectacular from Jaimez-Ruiz with the former Barnet shot-stopper clawing away a certain goal.
Jamie Clapham made no mistake 10 minutes later after curling home a direct free-kick from the same spot which left Jaimez-Ruiz with no chance.
Aldershot pulled ahead again on 76 minutes when Kirk Hudson found Scott Davies on the edge of the area and the midfielder drove in off the underside of the bar from 20 yards.
Seconds later, Hamshaw equalised after dancing into the box following a suicidal pass from Charles.
In the closing moments, Lillis produced a great low save from another long range Davies drive and from the corner Charles almost atoned for his defensive lapses by heading wide of the right post.