The Sky Blues picked up a point in their season-opening clash with the Glovers at Huish Park after Cody McDonald's early opener was cancelled out by a header from Yeovil's Richard Hines.
McDonald sent a bullet header past Yeovil 'keeper Marek Stech after nine minutes but Hines responded for the hosts midway though the first half.
It was the hosts that very nearly took the lead after six minutes when a free-kick floated into the Sky Blues' area fell to the feet of Richard Hinds who could only stab a bouncing ball over the bar from eight yards.
The Sky Blues took lead from their own set piece though after nine minutes with a powering header from McDonald.
Debutant John Fleck deserved almost as much praise for the delivery after McDonald drew the foul from Luke Ayling on the left flank.
Fleck whipped in a stunning outswinging delivery for McDonald who dived for the ball on the edge of the area and connected sweetly with his head to give Marek Stech no chance.
It was another free kick with 20 minutes gone which which almost gave the hosts the equaliser when Jamie McAllister's floated delivery into the box found the head of Reuben Reid who forced Joe Murphy to tip his header over the bar.
Yeovil were level from the resulting corner though when Hinds connected with an inswinging delivery to send his header past Murphy and just inside the foot of his far post.
Reid's ambition got the better of him two minutes before the half hour when his effort from 25 yards went well wide while McDonald and Fleck both had a chance to get City back infront three minutes later when McDonald went one on one with Stech who made the save with his legs and Fleck then gathering up the rebound and trying to finish from outside the area with Stech out of position only for Byron Webster to make a goalline clearance while covering for his 'keeper.
That was the last action for Fleck who was brought off holding his hamstring with 11 minutes of the half to go, Gary McSheffrey brought on in his place.
The Glovers went close again seven minutes before the break when Reid played a through ball for James Hayter whose heavy first touch in the area allowed Jordan Clarke just enough time to steal in and poke the ball behind just wide of Murphy's post.
It was Reid himself who was denied after 40 minutes when a quick route one ball from Ayling picked out the striker who's first touch took him past Reece Brown and in on goal, only for his half volley just inside the area to be kept out by a superb low one-handed save by Murphy.
The second half started with a flurry that saw the Sky Blues' appeals for a penalty turned down after 51 minutes when McDonald dispossessed Hines in Yeovil's area before appearing to be caught by the defender and going to ground only for referee David Phillips to wave away claims for a spot kick.
McDonald got in the mix again three minutes after the hour when he caught Ayling in possession and cut into the box, firing a low effort across the face of the goal and just wide.
City went even closer to regained the lead with 15 minutes to go when a one-two between Barton and Kilbane then paved the way for a measured first time effort from Barton which crashed off the far part of Stech's crossbar.
Clarke was on hand with a follow up from the edge of the area but sent his effort high over the bar.
Hinds then thought he had snatched a second for Yeovil after 80 minutes when he chested down a delivery in the box and half volleyed into the net on the turn. The home fans celebrated only to be disappointed after the goal was ruled out for handball.
The hosts carved out another chance two minutes later when a through ball from Dominic Blizzard found Reid who went one on one with Murphy but was unable to lift his effort over the onrushing 'keeper.
The Sky Blues had a glorious chance to win the game injury time when McDonald created an opportunity for himself thanks to his work rate, which had been impeccable all afternoon.
He hunted down Webster and caught him in possession in his own area but blazed his effort over the bar from just six yards out.
Coventry City: Murphy, Clarke, Wood, Brown, Hussey, Kilbane (c), Daniels (Jennings 84), Fleck (McSheffrey 34), Barton, Ball (Elliott 63), McDonald
Subs: Dunn (GK), Malaga, Baker, Edjenguele
Yeovil Town: Stech, Ayling, McAllister (c), Hinds, Webster, Blizzard, Upson, Hayter (Young 81), Reid, Foley (Ralph 77), ugwu (K Brown 60)
Subs: Stewart (GK), Young, C Brown
Booked: Reid (YEO) Hussey (COV)
Referee: D Phillips
Assistant Referees: W Bull, M Pottage
Fourth Official: A Tranter