The visitors took a two goal lead in the first half and although Jon Obika pulled a goal back in the second half with a superb long range effort, it is the Grecians who go forward into Round Two.
There was one change in the Town line-up with Jermaine Hylton missing out due to his injury sustained against Bradford so Fabien Robert started in midfield and Exeter included ex-Town player Ryan Harley in their starting line-up.
Exeter kicked off playing towards the Town End stand but it was Town who made the brighter start and had an early chance when Robert was fouled but Kasim’s free kick was easily dealt with by the Grecian’s defence.
Kevin Stewart was cautioned for delaying a free kick in the 10th minute after he unnecessarily stuck his foot out just three or four yards from the ball when the Exeter keeper Olejnik took the kick.
Town had a corner in the 14th minute when Harley deflected the ball behind but were unable to threaten even when the keeper misjudged the flight of the ball.
Exeter were relying on counterattacks and threatened in the 18th minute when Tom Nichols had a chance in front of goal but Vigoroux pushed the ball away and it was cleared.
Brandon Ormonde-Ottewill did well to clear a goalbound shot off the line in the 25th minute as Exeter exerted more pressure.
Town responded with some good attacking with Obika denied at close range by the keeper and then a shot by Stewart was deflected straight to the keeper in the 28th minute.
Nathan Thompson conceded a corner in the 34th minute, heading a dangerous looking cross behind to snuff out the danger but the Town defence cleared the resulting cross.
Town slipped behind in the 37th minute after being outnumbered in defence and the ball was flicked inside to Alex Nicholls who fired to the left of Vigoroux.
Disaster struck in the 42nd minute when David Wheeler fired home from close range after Vigoroux had pushed away a shot by Tom Nichols and the Grecians looked good value for their lead after making the most of their chances.
Town responded with some determined attacking which saw Olejnik push away a goalbound shot by Kasim as the match entered added time and at the other end Ribeiro went close with a rising shot shortly before the half time whistle was blown by referee Charles Breakspear.
Town went straight on the attack from the off with Robert trying his luck from close range but his effort was deflected for a corner which was cleared. Robert tried his luck again in the 50th minute but his effort was again deflected for a corner which was cleared.
The Robins had another corner in the 52nd minute which eventually led to Obika firing into the netting from close range.
Town had four corners in quick succession before the visitors cleared the ball downfield but the referee spotted an infringement off the ball and showed a yellow card to Arron Davies and awarded a free kick to the Robins but they eventually lost possession.
Will Randall replaced Robert in the 62nd minute as Mark Cooper looked to try and get back in the match.
Jon Obika scored a superb goal for Town in the 65th minute when he received the ball at his feet before spinning and firing a powerful left footed shot from 25 yards which flew past Olejnik and that lifted the noise volumes around the County Ground.
Nathan Byrne went close to levelling in the 70th minute with a deflected piledriver but the ball went agonisingly wide of the upright with Olejnik flatfooted.
Danny Butterfield was cautioned for a trip near the halfway line in the 71st minute as Town tried to launch another attack and that was the Exeter player’s last contribution as he was substituted by Matt Oakley.
Ryan Harley conceded a free kick in the 74th minute about 20 yards from goal but the resulting kick was cleared downfield.
Craig Woodman replaced Tom Nichols in the 75th minute but it was Town who upped the pressure leading to a shot for Williams but his effort went wide.
Will Hoskins replaced Alex Nicholls in the 80th minute for the visitors .
Kevin Stewart popped up in attack for the Robins but his deflected effort was saved by the keeper who dived down to his left.
James Brophy made his debut for Town in the 84th minute replacing Ormonde-Ottewill.
Town earned a corner in the 86th minute but the short corner routine only led to a goalkick for the visitors.
Obika earned a free kick in the 89th minute when he was fouled on the edge of the box and up stepped Yaser Kasim but his effort struck the wall and the ball went out for a corner but the resulting cross was cleared.
Town had two corners at the end of the added 4 minutes but were unable to find a way past the Exeter defence before the final whistle was blown.