All that separated the two sides was one save by Yeovil goalkeeper Marek Stech from Torquay left-back Tom Cruise during the shoot-out.
United were so close to winning the tie in normal time and led 2-1 with two goals from Ryan Jarvis, until James Hayter grabbed his second goal of the night and Town's second equaliser in the first minute of stoppage-time.
That took the tie into penalties, and Yeovil scored with all five of their spot-kicks, by Hayter, Ed Upson, Gavin Williams, Jamie McAllister and Keanu Marsh-Brown.
Lee Mansell, Nathan Craig, Billy Bodin and Rene Howe, who was sent on as a substitute just before the final whistle, all drilled home their penalties, but Stech's save from Cruise settled it.
Torquay manager Martin Ling contented himself with only four changes from the side which had started the win over Accrington Stanley last weekend – Danny Leadbitter, Cruise, Craig Easton and Jarvis were all promoted.
It was a very different story for Yeovil boss Gary Johnson. Injuries and suspensions had ravaged his squad, to the point where he was down to his last 13 senior professionals, with goalkeeping coach Gareth Stewart and two youth players, Will Agbo and Mitch Brundle, among the substitutes.
The Glovers must have counted themselves unlucky not to score at least once in the first half-hour. The main reason they did not was Aaron Downes, who was in top form at the heart of United's defence, winning a series of impressive challenges in the air and on the ground.
United, with Leadbitter making an uncertain start at right-back, took a while to find their feet, but when they did get their passing game going they were a threat.
When Leadbitter lost out to Hayter in the eighth minute, Poke did well to push his shot round the post for the first of half-a-dozen corners that Yeovil forced in the first half.
Hayter was also just off target with a right-foot shot from the edge of the area in the 17th minute.
The Gulls knocked the ball around nicely, Cruise and Craig to the fore, without producing any real penetration until the 25th minute.
Then, Craig and Danny Stevens combined to slip Billy Bodin away on the left and, just as he seemed to be running out of room on the by-line, he flicked the ball over Stech from the narrowest of angles and Jarvis was there to force the ball over the line.
A rare passing mistake by Cruise in the 32nd minute allowed Hayter to set Reuben Reid up for a shot with Michael Poke to beat, but the Gulls' goalkeeper parried the effort and then Downes did well to divert Marsh-Brown's follow-up for a corner.
Upson chested the ball down and volleyed over before Yeovil deservedly equalised in the 37th minute, even if it was a mistake by Poke that helped to create it.
The United goalkeeper came to take McAllister's free-kick from halfway and, although he had the ball in both hands, he dropped it under pressure in a crowded goalmouth and Hayter was there to stab home from eight yards out.
A vocal contingent of Glovers' fans helped to gee up the atmosphere, and both sides had chances before the interval. How Yeovil did not get anyone on the end of a Marsh-Brown cross was a mystery, considering only a touch would have done the trick. Then, in the 43rd minute Easton put Jarvis clear, only for Stech to deflect his shot wide when United looked odds-on to regain the lead.
Neither side allowed the ball to rest for a second longer than necessary, so the action continued fast and furious in the second half.
Leadbitter more than made up for his earlier uncertainty with a great sliding tackle to stop Korey Smith scoring after good work by Reid.
Moments after that 'save' United were back in front. Mansell found Stevens on the left on a pacy counter attack, he cut inside Dominic Blizzard, released Jarvis on the right and he took a touch before beating the advancing Stech coolly from 15 yards.
The game still looked like it had more goals in it, and Poke had to be smart off his line to make a brave save at the feet of Foley as Yeovil tried to respond to Jarvis' second goal quickly.
In the 69th minute, Jarvis nearly made it a hat-trick. Again Stevens was the provider from the left after good work by Craig. Stevens cut back on Blizzard, floated a cross to the far post where Jarvis hit a first-time volley which Stech did well to block at close range.
Johnson made a double-change two minutes later, sending on Byron Webster and Gavin Williams for Hinds in defence and Reid in attack.
In the 73rd minute Ling prompted a standing ovation for Jarvis when he took him off and sent on winger Niall Thompson. Bodin moved into the middle of United's attack.
Craig continued to pull the strings for the Gulls – one glorious diagonal pass to set Thompson away for a shot wide was right out of the top drawer.
There was no lack of effort or intent from Yeovil in the closing stages, but United's crisp and accurate passing looked like denying them the possession they needed to save themselves. That was until the first minute of stoppage time when, just after a strong punch and save by Poke from Hayter, Marsh-Brown crossed from the right and Hayter rammed the ball home from six yards out at the near post.
Torquay United (4-3-3): Poke; Leadbitter, Saah, Downes, Cruise; Easton (Howe 92), Mansell, Craig; Stevens (Oastler 83), Jarvis (Thompson 73), Bodin. Substitutes (not used): Rice (gk), Yeoman.
Goals: Jarvis 25, 57.
Yeovil Town (4-4-2): Stech; Ayling, Burn, Hinds (Webster 71), McAllister; Marsh-Brown, Upson, Smith, Foley; Reid (Williams 71), Hayter. Substitutes (not used): Stewart (gk), Agbo, Brundle.
Goals: Hayter 38, 90.
Referee: A Woolmer (Northamptonshire).
Attendance: 1,280.
