The Lambs, who were led superbly at the back by the inspirational Matt Redmile, frustrated a Morecambe side who are yet to find their feet in front of goal this season.
While happy to sit back and defend in numbers Tamworth, who came into the game on the back of two successive defeats, looked useful themselves on the break and could have sneaked the three points.
The closest Morecambe came to a goal was five minutes before the break when David Perkins was put through on goal by Wayne Curtis. His shot beat James Dormand and looked all the way as though it would be his first senior goal for the Shrimps, but the ball hit the foot of the post and bounced just out of reach of the onrushing Michael Twiss.
For the majority of the game however the Shrimps came up against the defensive strength of Redmile and co who were presented with far too many winnable headers until a late flurry almost brought Morecambe the win.
On 78 minutes more good work from Curtis led to Jimmy Kelly crossing dangerously into the box to present Twiss a great opening, but the striker volleyed high and wide from eight yards out.
With two minutes to go the Shrimps came close again when a Danny Carlton corner whistled across the six-yard box and was inches away from being met by the head of the diving Jim Bentley.
Despite conceding a great deal of possession Tamworth could have taken the full points with Bob Taylor arguably missing the best chance of the game.
Taylor, like Morecambe's Twiss is not having the best of starts to the season after a great 2004/05 campaign, was gifted a golden chance on 47 minutes. Free on goal 12 yards out his shot beat Ryan Robinson, but struck the left-hand post when he looked certain to score.
The post also denied Simon Hollis in the first half. After being found at the far post by a lovely Hugh McAuley pass Hollis struck his volley superbly but saw his effort clipped on to the woodwork by Robinson.