Tim Sills shot just over the bar early on but it was the visitors who took the lead on seven minutes as Kyle Storer shot past Nikki Bull after defender Brett Johnson scuffed his clearance.
Just a minute later, however, The Shots responded as Steve Watson's cross was met by Tobi Jinadu. His effort was blocked by keeper Chris Neal but Sills was on hand to put home the rebound.
The Shots took the lead as Darren Barnard took the ball through for Watson to go one on one with the keeper who blocked his shot, but this time Nick Crittenden responded by heading in the loose ball.
As The Shots pressed, Jonny Dixon shot wide while Hugh McAuley's free-kick was hit straight at the keeper.
Sill's second goal was ruled offside as Tamworth found their second through Bob Taylor.
Barnard's free-kick at the other end had the fans cheering as it was found in the roof of the net as both sides went into the break level at 2-2.
A Tamworth corner in the second half was nodded towards goal by Taylor, but keeper Ball reacted well to parry over.
On the hour mark, The Shots increased their lead when Jon Challinor tapped home at close range.
At the other end, Tristram Whitman headed over before The Lambs won a free-kick on the edge of the area. Player-boss and substitute, Mark Cooper stepped up but blasted over.
The Shots then doubled their lead after a neat ball from Challinor found Dwain Clarke who crossed in to find an unmarked Tyrone Smith who finished well passed Neal for the fourth.
Dixon also hit the side netting but The Lambs pulled another back when Chad Sheppard's ball found Taylor who headed home.
However, they could not find a fourth but as Tamworth scored three from four on target efforts, The Shots will surely be looking at their defence.