Carlisle had to be patient but it was a fine example of counter-attacking football which eventually earned them their three points as Magpies youngster Alex Gilliead marked a fine personal display with a deserved winning goal.
An early long range drive from Davies sailed high over the bar and another drilled shot from Grant flew past the post as Exeter had the better of the chances just after kick off.
Carlisle attacked with purpose through a run from Sweeney and Grainger took over with a fierce cross into the area. A deflection sent Wyke wide and his return delivery had to be hooked clear as Gilliead lurked.
A loose pass from Hery caused real problems as Holmes overlapped but Atkinson was alert and he made a vital block as a shot came in. Atkinson was the man on the spot again for the next delivery as he lunged forward to block from Grant as a flick took the keeper out of the game.
A push from Atkinson gave Holmes the chance to pop a free kick into the mix and Ribeiro went close with a flick which flew just over the angle of post and bar.
The Cumbrians used the right flank to create their first good opening as Gilliead beat two to get into the area. His deflected cut back was behind Wyke and Sweeney couldn't quite get there.
Exeter broke quickly as they regained possession and Wheeler lobbed a high ball to the back stick as away shirts arrived late. Holmes nodded it down but Grant failed to control his whipped volley.
Another good Grainger cross was grasped by Olejnik as Sweeney hesitated, and Gilliead left three in his wake as United started to find their feet. Wyke touched it with his back to goal and Hery rattled a skewed volley wide.
An intricate set piece routine brought a thundering drive from Davies, as Exeter crept forward and found they had men to spare in the Carlisle box, and Gillespie had to tip it over as it threatened to creep in.
Joyce rasped a long range shot wide and Gilliead sent one right at Olejnik after another winding run as good football kept Carlisle in the opposition half. But Nicholls was disappointed at the other end when his 35-yard free kick dipped over the wall and straight at the keeper.
More good stuff from Gilliead brought yet another cut back from the lively forward, as the game flowed from one end to the other, but it was behind everyone and the visitors sensed a chance to burst forward. They moved it quickly and Holmes sank to the floor with his head in his hands as his goal bound effort was tipped wide by the full length Mark Gillespie.
Midfielder Bastien Hery brought the crowd to its feet just before half time when he exchanged passes with Sweeney. It took him across the face of the 18 yard box and his through ball for Miller invited a shot. Butterfield stayed big to block it.
United sent the first warning shot of the second half with a toe poke from Gilliead which curled past the upright, and the same player curled a beauty of a cross into the six yard box but there was nobody there to apply a touch.
Things unexpectedly opened up for Luke Joyce 35 yards from goal and a clear sight of goal brought a thumping connection. Olejnik saw it late but he did enough to make the parry. Joyce then tried to turn provider with a clipped cross to meet the run of the unmarked Jason Kennedy. His downward header brought a superb one-handed save as Wyke looked for the loose pieces.
Gilliead tormented McAllister, urged on by the fans in the Paddock, as he went past him on three occasions in quick succession to put balls into the box, and a run of four corners kept the pressure on until a volley from Miller flew wide.
Gilliead set up Grainger for a shot from distance as Carlisle pushed on but it rose high and Olejnik was able to watch it away.
Exeter sat deep but they were undone with 13 minutes left to go when Hery spun away with the ball on the edge of his own box. Asamoah pulled into space and he took his time to allow players to get up in support as he jinked in and out of the box. Loan star Alex Gilliead checked his run and a perfect cut back brought a crisp shot and a first senior goal for the Newcastle United youngster.
Wheeler dragged a shot wide as he went into the box in time added on but that was that as United got back to winning ways on their home turf.
United - Gilliead (77)
United - Miller (61)
Exeter - McAllister (51), Tillson (78), Butterfield (89)
Carlisle United - Gillespie, Miller, Atkinson, Raynes (Archibald-Henville 44), Grainger, Hery, Joyce, Kennedy, Sweeney (Asamoah 73), Wyke (Rigg 85), Gilliead. Subs - Hanford, Dicker, Osei, McQueen.
Exeter City - Olejnik, Butterfield, McAllister (Hoskins 81), Ribeiro, Holmes, Davies, Nicholls (Tillson 69), Moore-Taylor, Wheeler, Grant (Morrison 56), Brown. Subs - Nichols, Hamon, Jay, Watkins.
Referee - Mr Tony Harrington
Attendance - 4,021 (130 away fans)