The Lambs captain grabbed the winner from a John McGrath corner to reward gutsy Tamworth for a battling and resolute performance against Paul Tisdale's side.
The two teams could not have had more contrasting starts to the season. While Exeter were unbeaten and riding high in fifth place, Tamworth have made a dreadful start, losing all three games and conceding 11 goals in the process.
Lambs manager Mark Cooper has acted quickly in a bid to stop the rot, bringing in Bradley Thomas and Gavin McCallum on loan from Yeovil and recruiting striker Taiwo Atieno from Dagenham. All three players came straight into the side as Cooper made six changes to the team that were beaten 4-0 at Dagenham and Redbridge last week.
For Exeter, Danny Woodards and striker Lee Phillips returned from injury with the latter named as one of the substitutes.
Cooper's changes seemed to work as Tamworth's first-half performance was unrecognisable from the shambles at Dagenham, although they did need Sean Bowles to produce two good saves to keep them level at half time.
His first came after 28 minutes when Jon Challinor teed up Jamie Mackie and his left-footed strike was superbly palmed away at full length by the Tamworth stopper.
Bowles produced an even better save in the 35th minute to again deny Mackie.
This time Woodards played in the Grecians striker but Bowles dived acrobatically to claw away the shot which looked destined for the top corner.
But Exeter certainly didn't have it all their own way and Jon Stevenson almost put the Lambs in front in the 25th minute but his close-range shot was saved by the legs of Martin Rice.
Debutant McCallum, who was impressive in the first half, also went close with a thunderous strike from outside the area that sailed inches over the bar.
Adam Stansfield had a good chance just before half-time when he found space inside the Tamworth area but he snatched at his shot and the ball bobbled harmlessly wide.
Some of Tamworth's build-up play belied their lowly status as they passed the ball at pace, making it an uncomfortable afternoon for the visitors.
But Exeter were still dangerous and Simon Weaver produced a superb covering tackle to deny Stansfield an easy goal in the 54th minute.
Exeter should have taken the lead a minute later but firstly Tom Kemp stopped Challinor's header on the line and then Bowles produced another superb save to deny Stansfield.
Exeter appealed for a penalty when Chris Todd's header from a Rice corner appeared to strike the arm of Graham Ward but the referee waved away their protests, and then Matt Gill's strike from the edge of the box flashed wide.
Thomas made a superb last-ditch tackle to deny Phillips in the 63rd minute when the Grecians sub looked certain to score.
Exeter were now throwing everything but the kitchen sink at Tamworth, but the hosts were standing firm, even though they looked more than a little shaky at times.
After weathering a ten-minute storm, the Lambs started to go forward and a Brad Thomas header from a free-kick struck the Exeter crossbar but the referee had already blown for an infringement. Then Stevenson went close with a fierce strike that just flashed wide.
Tamworth finally got the breakthrough they deserved in the 80th minute when Smith headed home a McGrath corner under the despairing body of Rice and the Lambs captain almost repeated the feat with another header from a McGrath free-kick two minutes later.
In the dying minutes, Graeme Law almost scored in his own net when he headed a Jones free-kick just past his own post but Tamworth held on.