Goals from captain Carl Heggs and a first for the club for substitute Tommy Johnson proved to be enough for the Lambs, despite the Shots pulling a goal back through Kyle Matthews.
Heggs put Tamworth ahead after just ten minutes when he was on hand from close range to tap home after Bob Taylor had headed a Kyle Storer free-kick back into the six-yard box.
But the Lambs did not build on their good start and the Shots went close when Kirk Hudson fired into the sidenetting and then forced a superb save from Sean Bowles when he caught the Lambs defence napping from a quickly taken free-kick.
Lewis Hamilton and Ryan Scott also went close with good efforts.
Tamworth brought on former Aston Villa and Celtic striker Johnson at half-time for the ineffectual Nathan Jackson and he made an instant impact.
Matt Redmile out-jumped the Shots defence to meet a Storer corner and Johnson forced home the loose ball from close range.
But Aldershot pulled themselves back into the game just three minutes later when Ryan Williams picked out Matthews, who beat Bowles with a neat finish with the outside of his boot.
Aldershot pushed for the equaliser with Williams and Nick Crittenden both firing wide and Bowles had to produce another good save to deny Ian Simpemba in the closing stages as Tamworth held on for a vital victory.