After a goalless opening 45 minutes, three second half goals condemned the Young Glovers to defeat.
Joel Randall netted the opener before two Will Dean penalties completed the scoring.
Played out in front of 209 supporters at Huish Park, Antonio Falanga’s side were unable to reproduce the form which saw them reach the fourth round last season.
In a first-half largely dominated by the visitors, Josh Key had the first meaningful chance of the game inside the opening 10 minutes.
Collecting Jordan Dyer’s cut back, the City player was only able to blaze over the bar from inside the box acting as an early warning for Town.
As the clock reached the 20th minute, goalkeeper Charlie Philpott – called up from the Under-16s in Tommy Scott’s absence – was at his best to tip James Dodd’s wide free-kick onto the bar after it evaded everyone in the middle.
With the Green and Whites unable to inflict any pressure on Dan Green’s side, the Grecians had their best chance of the half just before the half-hour mark.
Tom Hayes’ under-hit back pass allowed Brandon Parsons to slot an effort under the advanced Philpott, only for Charlie Fripp to clear off the line on the cover to ensure it remained 0-0 at the break.
Despite a change of ends, it wasn’t a change of fortunes for Yeovil who immediately found themselves under pressure and a goal down after 47 minutes.
Joel Randall coolly controlled in the box before firing a strike into the roof of the net giving Philpott no chance.
Now with a goal advantage, Exeter took control further as Josh Williams’ venomous strike flew just over the bar from 20 yards.
City went even closer past the hour-mark when Philpott produced an excellent reaction save to keep out Key’s shot from close range.
However, it was 2-0 just minutes later after Hayes hauled down Key in the box.
Defender Dean stepped up and although Philpott got a hand to his spot kick, the visitors’ lead was doubled.
Increasingly busy, Town’s stopper was at his best again to keep out Jordan Sparkes’ strike from the angle, before the young ‘keeper conceded a penalty by bringing down Sparkes with 77 minutes played.
Dean placed the ball 12 yards out once again and confidently found the back of the net for his second of the night to round off the scoring.
The final 10 minutes become little more than a formality as Exeter comfortably reached the second round, leaving the Young Glovers to rue what could’ve been.