Having impressively contained the hosts until the final 15 minutes, Nouha Dicko broke the deadlock to confirm the hosts’ advancement in the cup.
Subsitute Sam Surridge spurned the Glovers best chance, as Town narrowly lost out in the first ever competitive meeting between the two sides.
Darren Way moved away from the familiar 4-3-3 formation in favour of 3-4-3 in the West Midlands, making three changes in the progress.
Tom James and Omar Sowunmi slotted into a three-man Town defence at the expense of Keston Davies and Jake Gray.
In a final change from Saturday’s opening day defeat at Luton Town, Rhys Browne took to the wing in place of Olufela Olomola.
Up against the Championship’s summer big spenders, the green and whites produced a disciplined opening 20 minutes which restricted Wanderers to plenty of possession in their own half.
Unable to penetrate a resolute visiting unit and having only registered two off-target long range strikes from Connor Ronan, it was the Glovers who notched the first shot on target.
Lively on the left wing, Otis Khan jinked his way into a shooting position having cut inside, before driving an effort into the arms of Will Norris at the near-post.
In a recurring pattern, Wolves patiently stroked the ball around the immaculate Molineux pitch, only to be continually frustrated by a well-drilled Town.
With corners a rare opportunity to get the ball into the box, Danny Batth powered a header into the ground and harmlessly wide as Nuno Esprito Santo’s side failed to test Artur Krysiak in the first-half
As Town grew into proceedings further, Browne almost picked out Francois Zoko in the middle after weaving his way to the byline past Willy Boly.
Browne’s trickery proved to be the last meaningful action of an opening 45 minutes which saw the visitors comfortably contain their Championship opponents, with the central defensive trio of Sowunmi, James and Nathan Smith imperious.
Looking to increase the tempo after the restart the hosts engineered their best opportunity of the match on 48 minutes.
Largely a spectator in the first-half, winger Ruben Vinagre powerfully drove to the byline before dispatching a low cross, prompting Krysiak to pounce on the ball with Nouha Dicko closing in.
Keen to avoid the lottery of a penalty shootout the hosts increased the tempo as the game ticked past the hour-mark, as Dicko blazed a venomous strike over the bar.
With Saturday’s League Two encounter with Accrington Stanley in mind, Sam Surridge and Olomola were introduced for Zoko and Khan, as the visitors looked to add attacking potency to their defensive solidity.
The introduction of Surridge almost had the desired effect, only for the 19-year-old to spurn the game’s best opportunity after 71 minutes.
Neat passing from James and Browne freed up space for Connor Smith in midfield, allowing the Irishman to masterfully pick out Surridge inside the box only for the Bournemouth loanee to blast wide from a central positon.
A wake-up call for the hosts, Vinagre called Krysiak into action once again with a shot from the angle, before Yeovil’s defence was finally breached.
Jordan Graham’s tantalising delivery from a corner was too good to turn down for Dicko, who glanced a header into the far corner to end an evening of frustration.
As the Glovers piled forward in search of a late equaliser Dicko forced another fine save from Krysiak, with the referee’s whistle ending a brave performance from Way’s side against Championship opponents.
Wolves: Norris, Graham, Bennett, Batth, Boly, Vinagre, Edwards (Enobakhare 69’), Price, Dicko, Ronan (Saiss 81’), Bonatini (Jota 69’).
Subs not used: Burgoyne, Doherty, Coady, Miranda.
Yeovil Town: Krysiak, Alfei, James, Sowunmi, N.Smith, Dickson, Bailey, C. Smith (Gray 81’), Browne, Khan (Olomola 66’), Zoko (Surridge 54’).
Subs not used: Maddison, Mugabi, Davies, Santos.