An early goal from Jayden Stockley was cancelled out by Jordan Green before Alex Fisher put Town ahead.
Stockley then headed home with 15 minutes remaining as the match ended all-square.
Town manager Darren Way made one change to the side which lost to Colchester in mid-week as Jake Gray replaced Yoann Arquin on the wing.
Arquin joined fellow substitute Gary Warren on the bench, as the latter continued his return from injury, while Sessi D’Almeida retained the captain’s armband in central midfield.
Way was still unable to call on seven first-team players due to injury with Stuart Nelson, Omar Sowunmi, James Bailey, Alefe Santos, Wes McDonald, Diallang Jaiyesimi and Francois Zoko all side-lined.
Town’s players showed solidarity with Jaiyesimi after the forward suffered a serious knee injury against MK Dons by wearing white shirts during the warm-up with the message ‘let’s do this for DJ’.
Yeovil started on the front foot as both Gray and D’Almeida had shots blocked in the early stages but it was Exeter who dealt the first blow, taking the lead on nine minutes.
Good work by Hiram Boateng on the right-hand side saw him cross for Stockley who guided a header past Nathan Baxter from five yards out.
Tom James fired wide after Fisher’s clever knock-down as the Glovers looked to get back on level terms.
The home side continued to push forward as James’ long ball found Olufela Olomola via Fisher; the striker’s cross reached Alex Pattison who managed to get above his man but could only guide a header wide.
Town were persevering with their direct play and it nearly paid off in spectacular style as Fisher tried an audacious long-range volley that had Christy Pym worried before it landed on the roof of the net.
Four minutes before half-time Green exchanged passes with Olomola before putting on the afterburners and racing into the box, but his touch was heavy and Pym came out to claim.
The last Glovers chance of the half fell to Fisher whose first-time shot was straight at Pym.
Town came out for the second half much the brighter, they grabbed an equaliser when Bevis Mugabi’s clearance caused confusion in the Exeter defence, Olomola nipped in and squared for Green to knock home.
James nearly completed the turnaround as his diving header from a corner was cleared off the line.
Just after the hour mark the Glovers did complete the comeback as Pattison found Olomola who twisted and turned before firing the ball across to Fisher to slide home.
Fisher headed over from Carl Dickinson’s corner as Way’s men looked to drive home their advantage.
Showing heart and passion in defence the Glover’s looked to hold on to their 2-1 lead after a spirited fightback.
However it wasn’t to be as the dangerous Stockley equalised on 75 minutes from Dean Moxey’s cross with another header into the bottom right-hand corner.
Substitute Jonathan Forte had a shot saved by Baxter in the dying minutes and Mugabi brilliantly blocked Boateng’s effort in stoppage time as the game ended 2-2.
Yeovil Town (4-4-2): Baxter; James, Mugabi, Donnellan, Dickinson; Green (Patrick 90), Pattison, D’Almeida, Gray (Browne 81); Olomola, Fisher.
Bookings: Pattison 90, D’Almeida 90.
Subs not used: Phillips, Warren, Rogers, Arquin, Mahmutovic.
Exeter City (4-3-3): Pym; Sweeney, Croll, A Martin, Moxey; Law (Jay 76), Tillson (Forte 62), Boateng; Taylor, Stockley, L Martin (Holmes 69).
Subs not used: Hamon, O’Shea, Abrahams, Collin.