Notts County suffered their first home league de
Jake Taylor and Jayden Stockley fired the visitors into a two-goal first-half lead.
Jon Stead then pulled a goal back from the penalty spot but, despite sustained pressure on the Grecians' goal, they couldn't find an equaliser.
Kevin Nolan handed Liam Noble his first start since he rejoined the club last year, while there was a full debut for Noor Husin and a home bow for Matty Virtue.
Injured duo Richard Duffy and Matt Tootle made way, while Terry Hawkridge had to settle for a spot on the bench.
The visitors were handed an early opportunity to take the lead when Elliott Hewitt, playing alongside Shaun Brisley in central defence, was adjudged to have tripped Stockley deep in Notts territory.
Lee Holmes curled the ball into the area and it looked like the danger was over when Dean Moxey's shot struck the post.
But the ball rebounded straight into Taylor's path for him to tap into an empty net.
Notts were having to feed off scraps in their pursuit of an equaliser, seeing a number of shots blocked and a tame Jon Stead header easily saved.
At the other end they had Noble to thank for a heroic last-ditch tackle to deny Lloyd James, minutes before Lewis Alessandra saw his curling effort plucked away from the top corner by Grecians keeper Christy Pym.
And the stopper was in action once more as the half drew to a close, making a crucial save to deny Hewitt - not that he knew much about the defender's flicked header from a corner.
It had been a challenging half for the Magpies and their frustration was compounded a minute later when Stockley latched on to a long ball forward, twisted his way past Brisley and found the bottom corner from the edge of the area.
There were no changes at the break and the visitors pressed forward in their hunt for a goal to kill the game.
They nearly had one when Stockley played Holmes into the area, only for Hewitt to make a superb last-ditch block.
Stockley then curled the ball against Ross Fitzsimons' crossbar with a shot from the left.
Notts needed a speedy response and came close to pulling a goal back when Dan Jones stood up a cross at the back post for Alessandra to meet first time. His effort was nodded off the line by Moxey.
Nolan's first change saw Shola Ameobi replace Virtue and partner Stead up front.
Moments after the big forward's introduction, Noble won a free-kick on the edge of the area but Grant could only find the wall.
Grant was growing more and more into the game and, minutes after he had let the ball run across his body and seen his shot diverted behind for a corner, he saw a first-time effort held by Pym.
Liam Walker was now on the field, in place of Husin.
And it was the Gibraltarian's fellow sub Ameobi who gave the Magpies a route back into the game when Troy Archibald-Henville tugged him back as he tried to meet Noble's free-kick.
The referee pointed to the spot and Stead duly dispatched the penalty for his fourth goal in as many games.
Notts' tails were up and Walker was next to try his luck, seeing his curling effort deflected wide with 12 minutes to play.
Noble stroked the ball just past the post from similar range as the Magpies continued to apply pressure on the Grecians' goal.
And then it was Exeter's turn to go close, James rolling the ball narrowly wide from the edge of the area after linking up with Stockley.
Nolan's final change saw Carl Dickinson replace Brisley, who had required lengthy treatment in the aftermath of the penalty incident.
Noble flashed a shot inches wide of the angle between bar and upright as time continued to tick away from the home side.
And Stockley saw a similarly speculative effort clip the post on its way behind before Grant curled an effort straight at Stockley after receiving the ball in space down the left.
Notts were given four minutes of added time in which to find an equaliser and preserve their unbeaten home league record.
Walker drilled a shot wide, seeing his corner appeals waved away by the referee, as Notts pressed hard for their second goal.
But it wasn't to come as the Grecians left Meadow Lane with all three points.