A deflected shot was enough to hand Cambridge all three points on a disappointing day at Brunton Park.
United created the first chance of the day when Sweeney arrived late for a clipped ball into the box. His header dropped just wide of the upright as the assistant on the Pioneer Stand side raised his flag for offside.
Cambridge teased with some good possession play in the Carlisle half but Simpson was muscled out of a header as he sniffed following a patient and measured build up.
Two Cumbrian corners were well dealt with by the U's and the visitors burst forward on the break as they cleared the second with Donaldson in command. His through ball put Elliott on the chase but Young did well to cover and smother the danger.
A foul on Asamoah 23 yards from goal gave Dempsey a chance to have a go but his effort caught on the wind and sailed over the bar.
Midfielder Courtney Meppen-Walter did well with quarter of an hour on the clock when he picked up a loose ball and pushed for the edge of the box. Dunn moved across to gather his stabbed shot.
A dinked free kick caused chaos in the Cambridge box as O'Hanlon, Rigg and Meppen-Walter kept it alive with blocks and ricochets which pinged around in the danger area. A corner followed and Rigg was unlucky when his glanced header bounced back off the top of the bar.
Striker Derek Asamoah brought another save from Dunn as the Blues kept the pressure on when he tried one from distance and Cambridge enjoyed a rare attack when Donaldson found space on the left flank as the visitors looked for a response. Elliott climbed high but he couldn't keep his header on target.
A scuffed shot from Dempsey punctuated a long period of weather affected play but Archibald-Henville sparked a wonderful passage of play when he sent Grainger clear on the left flank. A reverse pass allowed Potts to cross low and Coulson was relieved to see his intervention whip wide of the post as his stopper looked on in anguish.
Forward Steven Rigg drilled another instinctive volley over the target as Carlisle continued to attack sporadically and Asamoah was next to be disappointed when his back stick delivery grew legs and flew harmlessly away.
An early second half attack brought a half chance for Elliott when Dunk found him with a pinpoint cross. O'Hanlon did enough to put him off as he tried to pick his spot.
The U's struck gold with their next attack when Elliott intelligently cushioned a high ball with his back to goal. Liam Hughes pulled the trigger as it rolled into his path and a deflection took it past Gillespie and into the bottom corner.
A wind assisted Dempsey corner had Dunn flapping as the big guns converged and Young recovered the loose ball to pop it back into the box. Sweeney got the header but Dunn completed the catch easily.
Chances were few and far between but substitute Sullay Kaikai opened a route through when he rode two challenges on the wing. His cut back brought a scuffed shot from Dunk which spun harmlessly away towards the corner flag.
A powerful header from Archibald-Henville was plucked out of the air by Dunn as he redeemed himself following a rash sprint off his line, and the keeper was in action again when he dropped low to stop a long range shot from Potts.
Cambridge - Hughes (48)
United - Young (69)
Cambridge - Kaikai (74), Elliott (78)
Carlisle United - Gillespie, Young, O'Hanlon, Archibald-Henville, Grainger, Meppen-Walter (Amoo 61), Potts, Dempsey, Sweeney, Asamoah, Rigg (Beck 79). Subs - Hanford, Thirlwell, Gillies, Brough, Hammell.
Cambridge United - Dunn, Tait, Taylor, Coulson, Donaldson, Champion, Elliott, Simpson (Kaikai 46 (Bird 79)), Hughes, Nelson, Chadwick (Dunk 46). Subs - Miller, Cunnington, Norris, Hunt.
Referee - Mr Mark Heywood
Attendance - 3,406 (199 away fans)