After a goalless first period, the Glovers took the lead immediately after the restart as Sam Surridge opened his Town account following good work from Jordan Green.
Rhys Browne doubled the visitors’ advantage with a confident finish before Otis Khan registered a quickfire third.
Youngster Jack Sparkes grabbed a consolation for the Grecians with 10 minutes remaining, but it wasn’t enough to stop the Green and Whites starting their cup campaign with an impressive victory.
Darren Way made five changes from the side that dispatched Coventry City at Huish Park three days previous, handing Surridge and Green their full debuts.
Elsewhere, Daniel Alfei and Tom James lotted into defence while Jake Gray partnered James Bailey in central midfield.
With both sides making widespread changes, it was a disjointed start to proceedings in front of a sparse crowd.
Following a lengthy injury delay as Exeter’s Luke Croll had to be stretched from the field of play following a clumsy Green challenge, it took until 12 minutes for the first real action of the half.
Lurking at the back post, Jake Taylor fired a fierce effort goalwards, only to be denied by Artur Krysiak who had narrowed the angle brilliantly.
In the ascendancy, former Glover Reuben Reid almost opened the scoring from 20 yards five minutes later, only for his curling shot to whistle past the post and wide.
After City’s opportunities, it was Town’s turn to trouble the deadlock through Gray.
The energetic midfielder first drove an effort into the arms of James Hamon following Surridge’s lay-off, before volleying wide of the target having burst into the box moments later.
An increasingly stop-start affair, it was the Glovers who were next to be forced into a substitution.
Top scorer Olufela Olomola had to be withdrawn following a forceful challenge from Troy Archibald-Henville which saw the Exeter defender enter the referee’s notebook.
Despite losing their four-goal striker, Way’s side ended the half on the front foot as Surridge burst into life.
The Bournemouth loanee first blazed a powerful strike over the bar from the angle, before seeing a shot destined for the bottom corner following Khan’s cut back blocked by a sprawling Troy Brown in virtually the last act of the half.
Third time lucky is the adage, and so it proved to be less than a minute after the restart for the Town’s striker.
Tenacious play from Green saw the attacker brilliantly win possession in Exeter’s box, retaining composure to then pick out Surridge who coolly slotted a first-time effort under Hamon to get off the mark in green and white.
Keen to avoid just their second defeat of the season, Paul Tisdale’s side searched for an equaliser as the half developed.
Matt Jay and Reid both guided efforts off target, before Krysiak punched away Lee Holmes’ whipped free-kick just past the hour mark.
But still looking a threat in the final third, Green slammed an effort into the side-netting before the Glovers doubled their lead with a quarter of an hour remaining.
Khan’s incisive through ball perfectly picked out the run of Browne, who emphatically drilled past Hamon for his second in as many matches.
Before the hosts had the chance to respond it was 3-0, as Khan added a goal to his assist.
Showing pace and trickery to burst past his man along the by-line, the winger defied the odds to pick out the far corner from a seemingly impossible angle.
The Glovers surrended a three-goal lead at St James Park towards the end of last season, and Town fans could’ve been forgiven for feeling a sense of déjà vu when Sparkes grabbed a goal back on 80 minutes.
However, City’s goal proved to be little more than a consolation as Town saw out the final few minutes to start the Checkatrade Trophy group stages in impressive fashion.
Exeter City: Hamon, Taylor, Moore-Taylor (James 58’), Brown, Croll (Kite 9’), Sparkes, Byrne, Archibald-Henville, Holmes, Reid (McAlinden 64’), Jay.
Bookings: Archibald-Henville 32’, Moore-Taylor 52’, James 90’.
Subs not used: Pym, Woodman, Tillson, Key.
Yeovil Town: Krysiak, Alfei (Nelson 86’), Mugabi, N. Smith, James, Green, Gray, Bailey, Khan, Surridge, Olomola (Browne 39’).
Bookings: Green 6’, Browne 52’, Surridge 75’, Khan 90’.
Subs not used: Maddison, Davies, Dickson.