Despite dominating the game and creating a host of chances, Exeter had to be content with a point.
And they twice needed to come from behind to secure a point against the plucky part-timers.
Exeter created a string of chances in the first half and should have been well clear by the break. Sean Devine's free-kick hit the wall in the opening minutes, but fellow striker Steve Flack could only head the rebound into the arms of goalkeeper Ryan Devine.
Les Afful then skipped in from the left and struck a curling effort against the crossbar.
It was one way traffic in the early stages. Dean Moxey's free-kick was flicked on my Santos Gaia and Devine found the net only for the effort to be ruled offside. Andy Taylor then went close for the Grecians when his shot was deflected into the hands of Ryan Price, and Devine struck a post with a powerful shot.
But City were stunned when they fell behind against the run of play. Marvin Brown whipped over a cross and striker Bob Taylor rose well to head home from close range.
Exeter deservedly pulled level in the 28th minute. Santos Gaia found Flack, who headed the ball to Devine, and the striker made no mistake with a low shot.
Dean Moxey then thumped a free-kick over the bar and with better finishing Exeter could have been well clear by half time.
After the break Tamworth were awarded a controversial penalty after only 45 seconds. Shaun Harrad was alleged to have been tripped by defender Chris Todd, and he picked himself up to score from the spot.
But Exeter again pulled level when Afful was tugged by Kyle Storer and Barry McConnell made no mistake from the spot.
Despite continuing to create chances, Exeter had to content themselves with a point.