Carlisle were undone by a flowing second half attack following a solid first half performance and they were disappointed to leave St James's with nothing to show from another disappointing away day trip.
Long balls from both sides asked early questions but the keepers were on their toes and able to deal with the threats which were posed.
United used Beck as a target man and he twice held play up for Dempsey and Asamoah to support. He did well on 6 minutes to cushion a ball and wheel away into the box. Asamoah clipped it to the back post and the big striker was disappointed when his header fell wide of the target.
City responded with a no-nonsense attack when Woodman was given space on the left. His cross had Bennett and Wheeler interested but Grainger recovered to put it behind for a corner.
A long throw from Grainger caused problems at the other end when Beck moved first to flick it on. Amoo had his back to goal and his shot on the turn was always going wide.
Quick movement in midfield brought a fast moving break from the hosts, as the game sputtered along in second gear, but the delivery had to be dealt with as Nicholls sent a low cross to the near post. Anderson kept his eye on the ball and hooked it away to safety.
Grainger's set pieces grew in importance as the midfield area tightened up and he found Archibald-Henville with a deep corner midway through the half. The header was firm but he couldn't keep it down.
The hosts lifted home spirits moments later when Woodman found a yard and curled a lovely ball into the box. Wheeler made a dive on the run but he sent his flying header right at the keeper.
Danny Grainger took control of a 28-yard free kick as the sides exchanged half chances and Hamon had to scramble as it threatened to creep in.
A huge ball forward from Archibald-Henville brought a great chance for Sweeney as Beck flicked it into his path. A spin from the midfielder left his marker for dead but he blazed a rising volley into the stands.
Good pressure from Carlisle just past the half hour brought a recovery from Asamoah as he kept the ball in play tight by the corner flag. Dempsey called for it and his first time cross brought a header from just eight yards out by Beck. It was a good opening but it flew just over the bar.
A ricochet off Grimes caused panic at an Exeter corner and Nicholls was unlucky when he pounced on a loose ball. His volley was fierce but Archibald-Henville stood strong to make the block.
Exeter finished the half on top and a Grimes free kick was eventually cleared behind by Brown as it skipped across the face of goal. Former-Blue Chrsitian Ribeiro thought he'd scored from the Grimes set piece which followed but Grainger somehow cleared the ball off the line as the header flew past Hanford. The same pair combined for the third dead ball routine in quick succession but Nicholls couldn't control the Ribeiro nod down and his shot spun harmlessly above the nets.
The Grecians started the second half as they had finished the first and a Grimes pass from deep had Nicholls shoulder to shoulder with Sweeney. The attempted clearance cannoned into Nicholls and Hanford had to dive low to prevent it from creeping over the line.
Exeter stayed forward and Hanford had to drag a Ribeiro cross from the beneath the bar as he scampered back to hook it clear. Nicholls was onto the loose ball and he fed it back to Woodman but the left back rushed his shot and drilled it into the side netting.
United were undone just before the hour when Grimes robbed Amoo of possession deep inside the home half. A neat exchange of passes left Scot Bennett with just Hanford to beat and he made no mistake as he kept his head and picked his spot.
The Carlisle reply was almost instant as Grainger threw another long ball towards the six yard box. Amoo got there but his glanced header edged just wide of the far post.
Nicholls and Grimes went close to extending the gap as they both found the side of the net, following a direct approach to football from the hosts, and Asamoah was penalised for a bump on the keeper as Carlisle showed attacking intent with a ball forward from Dempsey.
Substitute Billy Paynter almost found Dempsey with a dipping cross as Carlisle rallied late in the game and Anderson put his header from the corner over the bar as United pushed for an equaliser.
Harley rifled one at Hanford as the game ended with both sides on the attack and Potts went close when he thumped one just past the angle of post and bar.
But the points were secured by the Grecians when Wheeler fed Grimes to poke it past Hanford and into the back of the net after he'd left his marker for dead.
Exeter - Bennett (58), Grimes (89)
Exeter City - Hamon, Ribeiro, Butterfield, Oakley, Woodman, Davies (Harley 78), Grimes, Noble, Bennett, Nicholls, Wheeler (Cummins 90). Subs - Pym, Keohane, Nichols, Tillson, Morrison.
Carlisle United - Hanford, Brown (Paynter 82), Archibald-Henville, Anderson, Grainger, Thirlwell (Potts 69), Sweeney, Dempsey, Amoo, Asamoah, Beck (Robson 61). Subs - Eccles, Meppen-Walter, Brough, Symington.
Referee - Mr Oliver Langford
Attendance - 3,402 (162 away fans)