United had to come from behind on three occasions to get their share of the spoils but they just about deserved their point as their eye catching attacking display covered over a run of mistakes which threatened to cost them the game.
Carlisle started well and they fashioned an early chance when Grainger drilled a 30-yard free kick into the wall. Brough was first to the deflection but his volley, on his wrong foot, was easily cleared.
Left back Grainger was involved again when he used Ibehre and Thompson to make space and a whipped cross found Kennedy on the move. He connected with a firm header but he could only guide it wide.
The Cumbrians were rocked back after their good start when Dunk was given time to pick a cross into the box. Raynes lost the flight of the ball and Corr did the rest as he nodded a downward header into the bottom corner.
It sparked a good spell for Cambridge and another deep cross from Donaldson brought Dunk in from wide. It was a difficult chance and he wheeled away in disappointment as he put his header into the side netting.
The pressure stayed on from the away side and they doubled their lead when a deflected free kick caused panic in the home defence ranks. A spinning ball gave Corr a clean sight and Gillespie did well to make a point blank save. Coulson was next up, as he stabbed it back at the target, but Grainger was there to clear it off the line with his keeper well beaten. The danger was still there as Geroge Taft lurked on the edge of the area and he somehow squeezed his shot through a ruck of bodies and into the bottom corner.
Carlisle had to work hard to make things happen and a long range strike from Miller hit two on its way to the back post. Omozusi swept it clear before Brough could make any kind of contact.
More determined work from Carlisle brought another chance when Miller sent a cross at the penalty spot. A touch from Kennedy took it onto the post and shots from Brough and Wyke were blocked at source as Cambridge defended with their lives.
The hosts grew in stature after the miss and they got their goal when Miller hooked a half clearance into the box. Raynes nodded it down, Kennedy pushed it on and Ibehre did the rest with a lovely strike on the run.
The visitors sat back and the Cumbrians levelled the scores when Grainger whisked a lovely ball in from deep. Ibehre bagged his fifth of the campaign with a perfectly executed glance into the roof of the net.
There was a sting in the first half tail ahead of the break when a slip from Raynes on the edge of the area, following hesitation from Joyce and Gillespie, allowed Corr to burst through. He didn’t need to be asked twice as he stroked a cruncher past a dive from Gillespie.
Carlisle were back on level terms for a second time just five minutes after the break when a clip into the air from Raynes found Wyke with his back to goal. He spun his man and rattled a beauty of a finish past Beasant from 19 yards.
But the home side shot themselves in the foot again just before the hour when a wayward pass from Miller, on the half way line, left Cambridge with space to attack. A lucky deflection as Corr shot left Berry with the pieces to feed on and he finished emphatically to restore the one goal lead.
Thompson sent a difficult volley over when a Grainger free kick was cleared out of the box, and Carr did the same at the other end when he tried to outfox Grainger. The left back stood tall and forced the shot to be rushed.
United thought they'd equalised on 73 minutes when Osei recovered a blocked shot. His cross found Kennedy but his header beat both Beasant and the post as it skipped off the slick surface.
Carlisle deserved something from the thrilling encounter and in-form striker Jabo Ibehre came up trumps when he pounced on a poor clearance from a Grainger corner. He put his boot through it and celebrated in style as it bulged the back of the net.
Gillespie had to save from Carr and Taft as Cambridge built up a late head of steam, with the latter a push onto the bar from a thumping header, but the hosts also went close as Wyke challenged and a Raynes shot brought loud appeals for handball.
Both sides pushed for the winner and another loud shout for a penalty was waved away when Wyke was blocked, but it was a standing ovation which greeted the final whistle at the end of another unbelievable day.
United - Ibehre (42, 44, 76), Wyke (50)
Cambridge - Corr (11, 45), Taft (21), Berry (58)
United - Hery (30), Grainger (45)
Cambridge - Keane (4)
Carlisle United - Gillespie, Miller, Grainger, Raynes, Brough (Osei 58), Thompson (McQueen 75), Hery (Balanta 64), Kennedy, Joyce, Wyke, Ibehre. Subs - Hanford, Dicker, Archibald-Henville, Asamoah.
Cambridge United - Beasant, Omozusi, Keane, Roberts, Donaldson (Hughes 59), Berry, Corr, Dunk (Taylor 85), Coulson, Taft, Newton (Carr 66). Subs - Dunn, Simpson, Morrisey, Chiedozie.
Referee - Mr Richard Clark
Attendance - 4,833 (278 away fans)