The spirited hosts held their own against their more illustrious opponents, seeing one effort cleared off the line, a goal controversially disallowed and a penalty saved before Villa finally took the lead.
However, Conor Hourihane's goal 13 minutes from time proved to be the difference as Villa survived the scare at Huish Park, avoiding an ignominious early exit from the competition and sealing their best start to a new campaign since the 1960s.
Villa went into the match having won their opening two league games of a season for the first time since 1999, but they struggled to settle at Huish Park and it was the home side that started the brighter.
Some industrious work from Alex Fisher almost gave Yeovil the lead after 14 minutes when he raced on to a pass down the right channel and took the ball off Axel Tuanzebe before curling a fine effort towards the top corner which debutant Villa goalkeeper Andre Moreira needed to claw away.
Moments later the hosts almost took the lead in even more spectacular fashion when the ball dropped to Yoann Arquin, who showed great technique to fire a first-time volley narrowly over the crossbar from just outside the area.
The Glovers' failure to make the most of their positive start looked as though it could prove costly when Villa began to grow into the game midway through the half, and the visitors created their first real chance in the 25th minute when Andre Green pulled the ball back into the middle for Rushian Hepburn-Murphy, who snatched at his strike and put it well wide.
The Championship outfit were looking increasingly dangerous as their superiority began to show, but they struggled to create any clear openings and Yeovil came inches away from breaking the deadlock against the run of play 10 minutes before half time.
Villa's defence fell asleep for a lofted pass into the box which allowed Diallang Jaiyesimi to sneak in behind and knock the ball back into a dangerous area. Fisher picked it up with his back to goal but quickly swiveled and got away a low strike which Tuanzebe needed to clear off the line.
Tuanzebe had a sight of goal himself at the other end when he pulled away from his marker, but Villa's best attacking moment of the first half came moments later when Green created space to shoot before unleashing a powerful long-range strike which needed to be tipped over the top by Nathan Baxter.
Yeovil responded with a glorious chance just one minute later, though, as a simple pass forward sliced open the entire Villa defence and sent Jaiyesimi clean through on goal. The striker's first touch let him down, but some uncertain goalkeeping from Moreira almost kept the chance alive until Tuanzebe swept up the danger.
The hosts did have the ball in the back of the net from the resultant corner when Jaiyesimi tucked home from point-blank range after Omar Sowunmi's strike had been cleared off the line by Neil Taylor, only for the goal to be controversially disallowed for a foul by Gary Warren in the buildup.
Yeovil went into the break slightly aggrieved that they had been denied the lead, although they were on the right end of a contentious decision five minutes into the second half when once again Warren was at the heart of the debate, going unpunished for an apparent handball in the area.
The centre-back made two blocks in quick succession to deny Hourihane, but the second of those came off an outstretched arm on the ground which Warren appeared to deliberately extend.
Villa had another sight of goal shortly before the hour mark when Albert Adomah's cross was glanced wide by Ritchie de Laet, and two minutes later the Championship outfit found themselves facing the possibility of going a goal down when Yeovil were awarded a penalty.
Tommy Elphick was adjudged to have been too physical when defending a corner inside the box and referee John Brooks had no hesitation in pointing to the spot, but Fisher saw his subsequent spot kick well saved by Moreira, who up to that stage had endured an unconvincing debut.
Villa's struggles forced manager Steve Bruce to call upon the cavalry as Jonathan Kodjia and Jack Grealish were brought off the bench, and the latter almost made a spectacular impact just six minutes after his introduction when his dipping 30-yard strike crashed against the crossbar.
An end-to-end period of the game saw Wes McDonald and Alex Pattison both squander sights of goal for Yeovil either side of a chance for Green, who stepped inside his marker but dragged his finish wide of the near post.
The breakthrough finally arrived in the 77th minute, though, when Kodjia beat his marker down the right flank before playing a low ball into the box which Sowunmi could only deflect into the path of Hourihane, who was left with a simple finish from close range at the back post.
New EFL Cup rules for this season meant that one Yeovil goal would force a penalty shootout without the need for extra time, and the home side's fading hopes were given a boost when the fourth official indicated six minutes of added time.
Yeovil almost made full use of them too when a long throw was flicked on by Sowunmi in the 95th minute, only for Warren to fire his effort over the crossbar as the Glovers' final chance of an upset against the five-time winners of the competition disappeared.
Yeovil are back in action on Friday night when they take on Notts County, whereas Aston Villa travel to Portman Road to take on Ipswich Town on Saturday looking to continue their 100% start to the season.
YEOVIL (4-4-2): Baxter; James, Sowunmi, Warren, Dickinson; Arquin, Cole (Pattison 33'), D'Almeida, McDonald; Jaiyesimi (Henry 82'), Fisher (Rogers 85')
ASTON VILLA (4-5-1): Moreira; De Laet, Elphick, Tuanzebe, Taylor; Adomah, Hourihane, Whelan, Doyle-Hayes (Grealish 57'), Green (Bree 83'); Hepburn-Murphy (Kodjia 58')