Matt McClure stunned the hosts by flicking the Shots into a 1-0 lead after three minutes, but Tranmere hit back through Cole Stockton's sharp volley on the rebound nine minutes later.
Connor Jennings then fired Tranmere in front after being put clean through by James Norwood after 23 minutes, but Aldershot dug in and levelled up via Bernard Mensah five minutes before the interval.
Lois Maynard headed Liam Ridehalgh's free-kick wide as the hosts pushed late on, but they were unable to stop leaders Lincoln extending their advantage to five points.
Match report supplied by the Press Association.
Match ends, Tranmere Rovers 2, Aldershot Town 2.
Second Half ends, Tranmere Rovers 2, Aldershot Town 2.
Substitution, Aldershot Town. Manny Oyeleke replaces Jim Kellerman.
Jim Kellerman (Aldershot Town) is shown the yellow card.
Substitution, Tranmere Rovers. Andy Cook replaces Cole Stockton.
Substitution, Aldershot Town. Shamir Fenelon replaces Idris Kanu.
Connor Jennings (Tranmere Rovers) is shown the yellow card.
Substitution, Tranmere Rovers. Erico Sousa replaces Adam Buxton.
Kundai Benyu (Aldershot Town) is shown the yellow card.
Michael Ihiekwe (Tranmere Rovers) is shown the yellow card.
Second Half begins Tranmere Rovers 2, Aldershot Town 2.
First Half ends, Tranmere Rovers 2, Aldershot Town 2.
Goal!  Tranmere Rovers 2, Aldershot Town 2. Bernard Mensah (Aldershot Town).
Goal!  Tranmere Rovers 2, Aldershot Town 1. Connor Jennings (Tranmere Rovers).
Goal!  Tranmere Rovers 1, Aldershot Town 1. Cole Stockton (Tranmere Rovers).
Goal!  Tranmere Rovers 0, Aldershot Town 1. Matt McClure (Aldershot Town).
First Half begins.
Lineups are announced and players are warming up.
Tranmere lost ground at the top of the National League after Aldershot held them to a 2-2 draw.