Louis Soares ignited the game in the fourth minute with a trademark run from his own half.
He burst into the final third before delivering an exquisite pass to Ryan Williams on the left who returned the ball but the former Barnet man headed over from seven yards.
With David Lee restored to the line-up for the first time in over a year, the Shots produced some excellent possession football. Tamworth simply had no answers and were cut to pieces again in the 16th minute.
The lively Joel Grant combined with Williams and the winger's low drive forced Sean Bowles to smother the shot.
The pressure finally told in the 19th minute when Williams delivered an in-swinging cross to the near post. Grant ghosted into the box and planted his header into the top right corner past the despairing dive of Bowles.
Aldershot continued to dominate possession without seriously threatening the Tamworth goal and they were made to pay dearly for their lack of decisiveness in a three-minute period at the end of the first half.
In the 43rd minute Steven Burton levelled the scores with Tamworth's first serious effort on goal. Kyle Storer slid Burton through the middle and he curled his shot into the top right corner with aplomb.
A minute later the former Crawley Town player nearly doubled his tally. Taiwo Atieno played Burton in on the angle and his fierce drive from nine yards forced Nikki Bull into a great reaction save.
The Shots defence was still asleep and fell further behind as a result of the corner. John McGrath whipped an in-swinging corner to the far post which cleared everyone in the box and nestled into the net to the deafening silence of the Recreation Ground faithful.
Shots boss Terry Brown was clearly incensed by his side's complete loss of concentration and demanded a first-class response.
Former Premiership striker Marcus Gayle duly delivered. In the 51st minute Williams found Gayle from Darren Barnard's deep cross from the left and the former Rangers striker made no mistake with a header from five yards.
Gayle doubled his tally in the 54th minute as Soares' deflected shot fell to the striker's feet from 12 yards and he calmly slotted home in off the right post.
Seemingly in control, the Shots pressed the self-destruct button again. This time Storer fired an unstoppable 25-yard volley into the bottom right corner from a Lee clearance.
Bowles and Bull then produced stunning saves at either end as both sides pushed for all three points, but a point apiece was a fair reflection on a compelling encounter.