Carlisle started brightly but were made to pay for their missed chances when three first half goals in the space of 20 minutes effectively handed the home side the points.
An early pass from Elliott sent Hughes on a run down the left flank and his low cross had to be watched closely by O'Hanlon as he retreated. A clearance with the outside of the boot prevented Diallo from having a shot.
A free kick midway inside the home half allowed United to send men forward and Grainger didn't disappoint with a firmly struck delivery. All it needed was a touch as it curled across the face of goal.
The pressure belonged to Carlisle and Grainger had two crosses blocked at source as he tried to find a way through. His third attempt had more depth but O'Hanlon couldn't keep his header, from the edge of the box, down.
Cambridge responded with a long ball forward and Gillespie had to run out of his area to clear as Simpson broke through. It went straight to Diallo but his attempt at an immediate lob was always heading wide.
The corner count continued to rise for the Cumbrians and Marriott had a shor on the run blocked as he tried to find a way through. It fell nicely for Amoo and he cut back inside before rifling a left footer into the stands.
More good work from Marriott following a Symington cross created another opening as Sweeney called for it when he lost his man. He had to stretch and his toe poke shaved the bar as it flew past the keeper.
Carlisle were made to pay for not taking advantage of their bright start when Issa Diallo found a sweet connection from 25 yards. It flew through bodies and left Gillespie with no chance as it whistled into his bottom corner.
Potts went close at the other end when he drilled a lay off from Amoo a yard over, but Diallo and Simpson asked questions at the other end with instinctive snapshots which the Carlisle keeper had to deal with.
And the U's lead was doubled when Diallo turned provider with a clipped cross at the penalty spot. Robbie Simpson was in acres of space and his looping header crept under the bar as he wheeled away in celebration.
A free kick from a tight angle on the edge of the Carlisle box caused more problems as it pinged around inside the box with Diallo and Elliott both interested. A scuff from the former needed a palm from Gillespie to send it wide of the post.
Carlisle huffed and puffed, with Potts going close with another shot from the edge of the box which had too much height, but they were dealt a killer blow when Simpson started and finished a move on the stroke of half time. His pass released Elliott and the cross which followed left the nippy front man with the simple task of side footing it in to the empty net.
Nelson went close with an early second half header which dropped onto the roof of the net, when he rose highest at a corner, and Carlisle had an opening at the other end when Symington skipped down the wing and crossed deep. Paynter nodded it back into the mix but Elliott's attempt at an elaborate overhead kick was always going to be difficult.
A wild 19-yard strike from Paul Thirlwell followed, as United tried to get things going, but Hughes was close at the other end when Diallo fed a whipped cross to the far post. The big midfielder threw himself at it but he couldn't quite find the touch.
The game settled to a slower pace but a long ball forward released Elliott to go one on one. Gillespie was on his toes to try and catch him but a touch took the ball over the stopper and left him in no man's land. Elliott knew he had to go early but he couldn't get his volley at the open goal to hit the waiting target.
The U's looked good for their lead as they closed the game out and they rubbed salt into the wounds late in the day when substitute Jayden Stockley bullied his way onto a very well delivered cross from Taylor. His header had power and purpose and it flew into the top corner to send the home fans wild with delight.
And he doubled his tally from a Bobby-Joe Taylor free kick with just three minutes left to play when he once again used his power to claim the header which rattled the back of the net.
Cambridge - Diallo (25), Simpson (33, 45), Stockley (82, 87)
Cambridge - Diallo (43)
United - Sweeney (69)
Cambridge United - Dunn, G Taylor, Coulson, Donaldson (B Taylor 85), Champion, Elliott, Lanzoni, Simpson (Stockley 75), Hughes, Nelson, Diallo (Chadwick 60). Subs - Norris, Tait, Lennon, Hurst.
Carlisle United - Gillespie, Symington, O'Hanlon, Grainger, Brough, Potts (Gillies 59), Thirlwell, Sweeney, Amoo, Paynter (Dempsey 70), Marriott (Elliott 46). Subs - Hanford, Dicker, Rigg, Douglas.
Referee - Mr Carl Berry
Attendance - 3,512 (366 away fans)