After 210 minutes of action, Stoke City, who are over 80 league places above Tamworth, could not get the better of the part-timers and the two sides were still locked together after the mandatory five spot-kicks apiece.
Lambs full-back Michael Touhy saw his penalty saved by Steve Simonsen and Carl Hoefkens stepped up to stroke the decisive kick home and gift the Potters a home tie with Walsall in the next round.
The hosts looked like they were going to complete the shock of the third round as they hung onto a one-goal lead for 38 minutes.
Stoke created some great opportunities in the first half. Paul Gallagher wasted the best chance on 34 minutes when Dave Brammer drove a low cross into the six-yard box, but the on-loan striker hooked his shot over the bar from close range.
Two minutes later, Luke Chadwick fired in a fierce half-volley but Tamworth's giant keeper Scott Bevan was able to deflect it onto the bar.
But then, three minutes before half-time, the Lambs took a surprise lead.
Carl Heggs charged down a Michael Duberry clearance and latched onto the loose ball before crossing for teenage striker Nathan Jackson to stab home.
The 4,000 fans who packed into The Lamb ground went crazy and the impossible seemed to be a distinct possibility.
Stoke besieged the Tamworth goal in the second half and Gallagher went close with another fierce effort.
Home captain Adie Smith then produced a stunning block when Gallagher looked certain to score from close range.
Tamworth were hanging on and they rode their luck in the 64th minute when Marlon Broomes' effort struck the post and the Lambs managed to scramble the ball away.
The pressure finally told in the 80th minute when Tamworth failed to clear a Peter Kopteff corner and Gallagher hooked the equaliser home from close range.
Neither side could force a winner in extra-time and the game drifted into penalties.
Eddie Anaclet was the first to miss from the spot but Kevin Harper then had a kick saved by Bevan.
Poised at 4-4, the game was settled on the first round of sudden death penalties, much to Tamworth manager Mark Cooper's disappointment.
"I thought we were going to hang on and pull off a memorable shock," he said.
"The part-time players were magnificent and have matched a top Championship side over two games. I am so proud of every single one of them.
Stoke captain Duberry was relieved to get through.
"All credit to Tamworth because they really made it difficult for us," he said.
"The FA Cup is a great leveller and you couldn't tell the gulf between the two sides.
"We are delighted to be going through because that was a tough tie for us."