Exeter grabbed crucial goals at vital times to take the points on Saturday afternoon as Carlisle somehow came away with nothing to show from what was a decent performance.
United won an early corner but they were almost undone on the break when Harley surged into the area. HIs low cross was hooked away before Sercombe could pounce.
The Cumbrians had to be patient as they dealt with a lively opening from the visitors and a cross from Grainger fell right in front of Butterfield just six yards out. He had to poke it away as Rigg arrived late.
Exeter looked sharp on the break and things almost opened up for Harley as they burst out from inside their own box. The front man twisted and turned but Hanford was able to dive low to make the save.
Harley found another teasing low cross as he pulled wide on the left, with Morrison to help him out, but it was behind Sercombe and the moment was gone.
A measured build up from Young and Amoo left the wide man with space to exploit, as Carlisle edged on top, and he left two markers for dead as he turned on his heel. The angle was tight and Hamon had to keep his eye on it as a thundering shot angled for his bottom corner. The keeper parried and Butterfield completed the clearance as Rigg tried to get there.
Direct football from Exeter left Tom Nichols one on one with Hanford as a huge ball over the top bounced awkwardly. The young striker appeared to have done everything right until his placed shot bobbled past the upright.
Exeter took confidence from the attack and they grabbed the lead when a crossfield pass from Harley had Carlisle stretched. Alex Nicholls went for a cheeky lob as it opened up in front of him and Nichols was there to cut the rebound back as it bounced down off the bar. Harley had continued his run and he left Hanford with no chance as he rattled it under his dive.
Carlisle were back on terms ahead of the break when Amoo took his man on with a determined run down the right wing. His cross found Steven Rigg in shooting mood and his perfectly timed volley nestled sweetly in the bottom corner as he wheeled away in celebration.
United started the second half on the attack and a Wyke volley, with his back to goal, was blocked as he tried to swivel on the shot. The ricochet fell for Rigg but he blazed a wild one over the bar as he tried his luck from distance.
Sercombe and Dempsey exchanged deflected shots as the action started to move from end to end and Tom Nichols had to be stopped as he ran past three challenges and into the danger area.
But the visitors regained the lead when Harley checked his run as Nicholls took control on the right. His cut back was perfect, and the shot matched it as Harley doubled his tally for the day with a precise effort which bent into the bottom corner.
Carlisle threw men forward, with Gillies and Rigg probing at every opportunity, and Dempsey was thwarted when he pulled the trigger following another bout of battling for the ball.
Charlie Wyke was next to go close when he spun on the spot and let fly, but Hamon was well placed and he palmed it away as he moved across to deal with it.
Substitute Graham Cummins sent a shot at Hanford as the Grecians soaked up the pressure and broke in numbers, but everyone in the ground thought Dempsey had scored when he was first to react to a loose ball. His volley took the slightest of deflections and that was enough to push the ball wide.
Exeter delivered a killer blow in time added on when they broke, after a Gillies free kick had been tipped behind for a corner, and Sercombe was there to take it forward and clip it over Hanford as he raced off his line.
United - Rigg (39)
Exeter - (Harley 31, 56), Sercombe (90)
United - Archibald-Henville (80)
Carlisle United - Hanford, Young, O'Hanlon (Asamoah 75), Archibald-Henville, Grainger, Amoo, Griffith (Meppen-Walter 67), Dempsey, Sweeney (Gillies 37), Rigg, Wyke. Subs - Spiegel, Paynter, Thirlwell, Brough.
Exeter City - Hamon, Butterfield (Oakley 57), Ribeiro, Sercombe, Davies, McAllister, Moore-Taylor, Nichols (Wheeler 86), Nicholls, Harley, Morrison (Cummins 77). Subs - Bennett, Keohone, Pym, McCready.
Referee - Mr Tony Harrington
Attendance - 3,724 (154 away fans)