The festive fixture run continued on Thursday evening with an away trip to the Alexandra Stadium for the Blues.
Manager Paul Simpson was able to name an unchanged 18 following the Boxing Day home win over Bradford, with Jack Stretton once more at the lead of a front three.
There were huge ironic cheers from the home fans with just 45 seconds on the clock when Joel Tabiner sent a shot on target from 25-yards - something they hadn't managed to do at all in their Monday away match against Stockport.
A hefty challenge at the other end left Gibson with the ball at his feet and he tried his luck, again from distance. It scuffed off his boot and he dragged it wide.
Good football from the visitors saw Moxon and Guy switch it from the left flank for Gibson to deliver. He whipped it in and Offord had top put it behind on the stretch. The delivery from Moxon was excellent, and Morgan Feeney got enough on it from an initial touch from Huntington to guide it into the bottom corner.
There was chaos in the home defence when a lobbed ball forward from Guy bounced high on the edge of the area. Offord tried to nod it to the keeper, but Stretton got there first. His toe poke was fingertipped by Okonkwo, and that diverted it behind.
United had throws and corners to defend through a testing spell, but the target remained untroubled as the blue wall stood strong.
Wonderful skill from Moxon in midfield saw him spin and drag twice as he moved into space. He picked out Gibson, who caught Ellis on the overlap, but his delivery was charged down.
Crewe had a decent spell midway through the half but once again it didn't really cause concern as clearances and interceptions ruled the day.
Carlisle played some good football as they continued to press forward, with short passes helping to find the gaps. Armer was sent wide after one such exchange but the slightest of touches took the centre beyond Gibson as he steamed in at the back stick.
Much of the play was in the middle third, but the Cumbrians were almost gifted a goal when Gibson hunted his man down to steal the ball. Stretton raced into the area, and he kept his shot low as he aimed for the bottom corner. Okonkwo parried, and Gibson opened his legs to try to get the tap in. The keeper was up smartly to push it onto his shins and it ricocheted harmlessy behind.
A run from Agyei took him past Ellis just before the break, but he chose to shoot when he had options left and right. It was always going high.
Tabiner drew some oohs from the home contingent when he cut inside with the ball at his feet. He let it go from distance and Holy dived, but it looked like the keeper had it covered.
Another good Moxon free kick found Feeney on the jump just before the break, but his header put it behind the advancing wall, and Sambou sent it on its way.
There were just 45 seconds on the second half clock when the away lead was doubled. Harris popped a neat throw to Gibson. His high, drop of a delivery was nodded back into the mix by Armer, and Moxon showed great composure as he controlled it before clipping it over the line off the inside of the post.
It got worse for the Alex on 51 minutes when Offord launched a hand at Stretton. The referee had no hesitation in showing a straight red card.
Carlisle were patient in their build upon the hour with Hilton using Moxon as an outlet. Gibson asked for it, but his effort from range spun clear of the target.
The Cumbrians were up for it and a flighted pass from Moxon saw Hilton cause problems. McDonald had to see it behind, but the half clearance from the corner found Guy in a deep area. His volley had to be stopped or it was going in.
Some of the play on the ground from United was outstanding, and Harris, Hilton, Devitt and Guy sliced through to set Armer up for a 28-yard volley. He turned away quicky as it miscued itself into the ether.
Armer made immediate amends when he rifed the ball from deep for Dennis to claim on thre halfway line. The striker took nit first on his knee, and that left the defenders in his wake. A second touch was cute, and his third was an unstoppable effort that sent the travelling contingent wild. It was goal number 13 of the campaign for the forward.
The Blues were a whisker away from number four when Feeney jumped to meet a floated corner. Okonkwo was beaten and very relieved to see it strike the outside of his upright.
Carlisle continued to look the more likely, and there was almost a wonder finish from Jamie Devitt when he set himself late in the game. His fierce dipper from 28-yards crashed onto the underside of the bar and McDonald was able to mop it up.
Clever play in time added on from Dennis released Sho-Silva, and just for a moment he was clean through. The ball stuck on the surface and he was robbed just as he shaped to finish it off.
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Goals
Carlisle United - Feeney (6), Moxon (46), Dennis (72)
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Bookings
Crewe Alexandra - Mellor (49)
Offord sent off - 51 minutes (violent conduct)
Carlisle United - Feeney (26)
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Teams
Crewe Alexandra - Okonkwo, Mellor, Adebisi, McDonald, Offord (c), Thomas, Agyei, Sambou, Uwakwe (C Finney 86), Tabiner (Brook 68), Evans (Griffiths 54). Subs - Richards (gk), O Finney, King, Holicek.
Carlisle United - Holy, Feeney (c), Huntington, Mellish (Devitt 70), Ellis (Harris 46), Moxon, Guy, Charters (Hilton 58), Armer, Gibson (Sho-Silva 76), Stretton (Dennis 58). Subs - Kelly, Whelan.
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Match officials
Referee - Andy Haines
Assistant Referee 1 - Kevin Morris
Assistant Referee 2 - Johnathon Bickerdike
Fourth Official - Ruebyn Ricardo
Observer - Iain Siddall
Coach - Michael Jones
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Attendance - 4,493 (820)