The Lambs tested the Shots early on winning the corner when Bertie Brayley's clearance sailed to Matt Redmile who put the ball back into the mix and shots keeper Nikki Bull collected from Simon Ho'lis' rising header.
The Shots went close as Lambs skipper Aaron Brown hauled down Chris McPhee just a yard outside the area. Ahmed Deen curled in a shot that just missed the corner of the net.
On 16 minutes the visitors took the lead from ex-Shot Hugh McAuley's free-kick. Julian Alsop nodded down for Brown to head past Bull.
Six minutes later it became two as Adie Smith got the better of Hassan Sulaiman to square the ball for Hollis, who in acres of space slotted the ball into the bottom left corner.
While the home side had little going forward, the Lambs continued their attacks with Alsop twice heading towards goal only to see both efforts well saved by skipper for the day Bull.
In the second half the Lambs almost made it three as John Brough's back pass was intercepted by Tristram Whitman, he broke forward to go one on one with Bull who did just enough to put the midfielder off as he shot wide.
In what was to be one of those days Brayley headed against the bar before the home side finally registered their first shot on target on 55 minutes, Brayley shooting into the keeper's waiting arms.
Michael Gordon shot on the volley, but was again denied by the Lambs keeper.
Bob Taylor went close at the other end after a one on one with Bull, the keeper blocking the effort once again.
McPhee had the home crowd cheering late on with a goal, only to see it ruled out for offside as Tamworth went home with all three points.