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.

Brent and US crude futures fell below $45 and $40 a barrel respectively as global investors assessed the contagion risks of China's volatile stock market.
Recent data has suggested that China's economic growth continues to slow down.
As well as the volatility in Chinese shares, there are fears of a protracted effect on demand for commodities.
China's slowdown is expected to pull down other regional economies, affecting energy and raw material consumption.
The unstable Chinese market has also led to worries that the problems in the world's second largest economy may have far-reaching global consequences.
China's benchmark Shanghai Composite index on Monday shed as much as 8%, while markets in Hong Kong, Tokyo and Sydney all dropped by more than 4%.
On Friday, figures showed China's factory activity in August shrank at its fastest pace in more than six years.
Official figures have indicated that China's economic growth is continuing to slow. For the three months to the end of July, the economy grew by 7% compared with a year earlier - its slowest pace since 2009.
Bernard Aw, market strategist with trading firm IG, said given the tepid demand, it was hard to fathom why oil producers were pumping out more crude.
Opec producers, notably Saudi Arabia, and Iraq were producing more oil than necessary, while US stockpiles were nearly 100 million barrels above the five-year seasonal average.
"At this rate, the fundamentals of oil are going to get worse before it gets better as the supply glut widens. This means we are likely to see more weakness in oil futures in the coming sessions," Mr Aw said.
Oil dealers are also anticipating revised US economic growth data for the second quarter, to be released on Thursday.
The figures could be key to the Federal Reserve's thoughts on when to raise interest rates.
An eventual interest rate rise is expected to strengthen the US dollar, which in turn would make dollar-priced oil more expensive for buyers using weaker currencies, once again affecting demand.
Tranmere lost ground at the top of the National League after Aldershot held them to a 2-2 draw.
[NEXT_CONCEPT]
Oil prices have slumped to six-year lows as global stock markets continue to fall on concerns over a slowing Chinese economy.