City edged out a tightly contested encounter with Newport County thanks to a second half header from Tim Dieng.
City found the breakthrough in the 71st minute as a dangerous Jack Sparkes free-kick found the head of a lurking Tim Dieng who found the bottom left corner.
County Midfielder Finn Azaz had chances in the first half to put the hosts ahead, though City held strong throughout. Cam Dawson rarely had a save to make as the 1017 City fans were sent home to Devon happy.
Matt Jay was the only change for the Grecians, with Tim Dieng retuning to the team after missing out on the squad at home to Stevenage.
A quiet opening ten minutes failed to dampen the lively away support as City aimed to break the deadlock early.
The best chance of the opening stages fell to Newport as Azaz broke through following a ball lifted over the top of the City backline. Cam Dawson and Archie Collins both combined to ensure that County didn’t find the opener.
Minutes later there was another breakaway from the Exiles, as former Grecian Scott Bennett fired wide from inside the box.
The chances kept coming for the opponents, as Azaz was presented with his second chance of the match in the 27th minute, but once again Dawson was there to see off the danger.
The 35th minute produced a half-chance for the in-form Jevani Brown as the striker attempted an acrobatic overhead from the right of the Newport goal, unfortunately for City misfiring high and wide.
The following stages presented few chances for either team, as both searched for a late first-half breakthrough.
On the verge of the half-time, Archie Collins whipped a teasing corner from the left which allowed Sam Stubbs to break away from his marker at the far post and fire narrowly wide of the target.
The second period started in a familiar way, with Newport the team looking to apply the pressure to their opponents.
The 57th minute saw City produce their first shot on target as Jack Sparkes tested Joe Day in the Newport goal, firing straight at the keeper from long range.
Just a couple of minutes later, another chance came the Grecians way as a right corner delivery from Jevani found the head of Dieng who is unable to properly connect at the far post.
Enthusiastic support from the away end was pushing City to find a breakthrough. A couple of corners came and went for the away side with no end result.
With few chances for either team, the 71st minute saw City awarded a foul after Dieng was dragged down to the left of the opposition box. A Jack Sparkes cross delivered into the centre of the box found the head of Dieng and his low driven header found the bottom left of the County goal.
Following this, Newport looked for an immediate response, pushing players forward in a committed effort to draw level. Dominic Telford found some space in a crowded box but was only able to find the lively City supporters thanks to a block from Sparkes.
The match looked to be petering out in the closing stages, as Newport continued to search for a leveller. The Exiles continued to pass the ball around the edge of the Grecian box with Alex Hartridge being called upon with an important block to prevent a last-gasp equaliser.
A left sided corner for the opponents in the 88th minute allowed Courtney Baker-Richardson to produce a low driven header towards the left corner, but Cam once again came up with a strong save to stop the opponents. City would then see out the final few minutes for a huge three points.
The Grecians are next in action away at Carlisle United next Saturday, April 9 in a 3pm kick-off.
Newport County AFC: Day, Norman, Demetriou ©, Clarke (Street 89’), Lewis, Bennett (Collins 73’), Willmott, Azaz, Waite, Telford, Fisher (Baker-Richardson 61’)
Subs: Townsend, Haynes, Dolan, Ellison
Exeter City: Dawson, Key, Sweeney ©, Hartridge, Stubbs, Sparkes, Collins, Rowe, Dieng (Coley 84), J.Brown, Zanzala (Phillips 80’)
Subs: S.Brown, Diabate, Caprice, Coley, Jay
Referee: Christopher Sarginson
Attendance: 5,697 (1,017 away)