Second-half strikes from Francois Zoko, Shayon Harrison and Alex Lacey fired Town into an impressive lead, before a dramatic finale.
With 89 minutes on the clock, David Wheeler gave City faint hope before Troy Brown’s header a minute in five added on gave the hosts real belief.
And, just four minutes after Wheeler’s strike, Exeter drew level through Reuben Reid to rescue a point and leave the Glovers deflated.
Undefeated in their last three games, Darren Way made one change to the side that was frustratingly held to a 1-1 draw last time out at home to Accrington Stanley.
Harrison replaced Tom Eaves in the front two, in a bid to add a goal scoring edge to the Glovers effective approach play.
Bathed in sunshine at St James Park, both goalkeepers could enjoy the sun as much as the spectators in the opening 20 minutes, with chances at a premium.
Looking to retain their spot in the play-offs, the Grecians threatened to sustain a spell of pressure as the half grew on, only to be thwarted by a Yeovil side defending well as a collective.
Untroubled until almost the half-hour mark, Artur Krysiak’s first notable involvement was to routinely collect Ollie Watkins’ deflected effort, triggering a similar occurrence at the other end.
After neat build-up, Ben Whitfield’s shot from the edge of the box lacked the power to truly test Christy Pym, who comfortably gathered the ball diving to his right.
In an even opening 45 minutes in Devon, the Glovers grew into the game and almost went into the break with the lead but for a superb Pym save.
Matty Dolan’s deep free-kick was flicked on by Zoko into the path of Harrison, whose flicked effort was clawed out for a corner by the sprawling Exeter stopper as Town ended the half positively.
After a first half largely lacking in goal scoring opportunities, the second period burst into life immediately.
Krysiak had to be alert from the get-go, stretching every sinew of his 6’4” frame to acrobatically get a hand to Bevis Mugabi’s miscued clearance which was destined to loop over the Polish ‘keeper.
Keen to show his former club what they’re missing, the 27-year-old was in imperious form and with 50 minutes on the clock produced another stunning save to get a hand to Watkins’ low drive from inside the box.
Now an end-to-end affair, the visitors had a penalty claim waved away when Harrison went down in a bundle under challenge from Troy Brown, before Krysiak palmed away a venomous Watkins shot from the angle.
Unable to find a way past their former employer, Way’s side silenced the 4,600 home supporters with 62 minutes on the clock.
Having tenaciously won back possession, Dolan’s inch-perfect through ball picked out the run of Zoko who clinically curled an effort past Pym into the bottom corner.
Buoyed by taking the lead, Krysiak almost put the icing on the cake to his return to Devon with a goal, as his long clearance had to be tipped over for a corner by a scrambling Pym.
Staring an unexpected defeat in the face, the hosts emptied their bench of strikers and threw caution to the wind, but it was the Glovers who continue to threaten.
With 71 minutes played, Town won back possession once again and after Pym couldn’t handle Whitfield’s swerving drive, Harrison followed in to loop a header over the stranded City goalkeeper to notch his first senior goal.
Over 800 Yeovil fans made the short trip across the border and as they created a raucous atmosphere in the stands, it was 3-0 on 78 minutes when Alex Lacey rose imperiously to head home Dolan’s angled free-kick.
The Green and Whites were rampaging when substitute Jean-Louis Akpa Akpro was denied by a fine Pym save, before Exeter found themselves a lifeline.
With 89 minutes on the clock and after a spell of pressure, Wheeler’s shot from the edge of the box flew in off the post, sparking an unlikely comeback.
Five minutes additional time further buoyed the home crowd and with only a minute of the added time played, Brown reduced the deficit to one with a powerful header.
Now with a point in their sights, City seemed to have a monopoly on possession and after the ball fell to former Glover Reid at the back post, the striker emphatically picked out the back of the net.
The Grecians fancied a winner in the final few seconds as a shell-shocked Yeovil held on for a point in a game which will leave the Green and Whites wondering how all three weren’t returning to Somerset.
Exeter City: Pym; Sweeney, Brown, Moore-Taylor, Woodman (Reid 69’); Taylor (Wheeler 45’), James, Tillson, Harley; Watkins, McAlinden (Stacey 58’).
Bookings: James 77’
Subs not used: Olejnik, Grant, Oakley, Croll.
Yeovil Town: Krysiak; Shephard, Mugabi, Lacey, Dickson; Dawson, Butcher, Dolan, Whitfield (Goodship 90’); Zoko (Eaves 89’), Harrison (Akpa Akpro 75’)
Bookings: Dolan 45’, Krysiak 74’
Subs not used: Maddison, James, Bassett, Eaves, Sowunmi.