Visitors Crewe made it four wins from five games as they struck either side of the break to leave Carlisle with much to think about from another disappointing performance.
A strong run from Proctor earned United a free kick with three minutes on the clock and it almost brought a goal as the Adams delivery skimmed off Nugent. Keeper Ben Garratt readjusted quickly to tip it over the bar.
Adams was quickly over to take the corner and he spotted Grainger unmarked on the edge of the box. His volley was crisp but it was blocked before it could trouble the target.
The visitors responded with a good move of their own when Cooper fed a ball through to Bingham. He teed it up for Jones to shoot but he couldn't keep his effort down.
Crewe pushed on again moments later and Bakayago was given space to drop a high ball into the box. Bowery jumped high but he was disappointed to see his cushioned header drop the wrong side of the upright.
United had a goal chalked off for offside just before the quarter hour when Adams whisked another excellent free kick into the mix. Proctor guided a header into the bottom corner but his celebrations were cut short as the flag was raised.
The game was played at a pulsating pace, and both sides enjoyed decent spells of possession, but it was Carlisle who played the better football with some crisp passing keeping the Railwaymen on their toes. One such move brought Joyce to the edge of the box and he tested Garratt with a toe poke which flew right at the stopper.
Crewe came back into it on the half hour when Dagnall pulled wide to make a gap. Cooper shouted for it and his shot, which came immediately after he had trapped the ball, whistled just past the angle of post and bar.
United were dealt a blow before the break when Cooke stepped forward to play a one-two with Bowery which took him through the last line of defence. He kept his eye on the lobbed pass and left Gillespie with no chance as he swept a first time volley under the keeper's dive.
Carlisle went in search of a response and a Shaun Miller attempt brought a full length dive from Garratt as he headed a cross from Grainger at the bottom corner. The keeper did well to palm it round the post.
Gillespie was in action again at the other end when Dagnall went on the dive to meet a low delivery from Bakayago with his forehead. It was going in until the keeper spread himself to parry it.
Things got worse for United early in the second half when Shaun Miller was given a straight red card when he went into a challenge with Turton on the half way line. Referee Mr Miller took his time to think about it but he eventually produced the card and sent the forward down the tunnel.
Carlisle reshaped and a shot from Lambe from 20-yards flew through bodies and had to be dealt with by Garratt.
More injury woes followed as Nicky Adams left the field of play clutching his hamstring and Crewe took advantage with immediate effect as they attacked down the right wing. A cross from Cooper went under Dagnall's boot but Bowery was there to tap it into the empty net.
Lambe and Joyce sent shots at Garratt as United tried to build up a head of steam and Proctor had another goal ruled out for offside as he once again put a volley into the bottom corner.
A deflected Cooper effort went over the bar at the other end, and Garratt saved a firm strike from Proctor to maintain his clean sheet.
Gillespie made an excellent save late in the day to deny Cooke as he broke through to go one on one, and a late Grainger free kick stuck in the wall only to be hacked clear as Waring tried to make it count.
Crewe Alexandra - Cooke (34), Bowery (61)
Carlisle United - Proctor (83), Waring (90)
Sent off - Shaun Miller (51)
Carlisle United - Gillespie, T Miller, Liddle, Raynes (Waring 63), Grainger, Lambe, Joyce, Devitt (O'Sullivan 69), Adams (Joachim 58), Proctor, S Miller. Subs - Crocombe, Ward, Brisley, Hooper.
Crewe Alexandra - Garratt, Turton, Ray, Nugent, Jones, Dagnall (Ainley 90), Cooper, Bakayogo, Bowery (Wintle 84), Bingham, Cooke. Subs - Dawber, Udoh, Ng, Dale, Finney.
Referee - Mr Nigel Miller
Attendance - 4,695 (357 away fans)