United were at Holker Street for their penultimate away fixture of the season on Saturday afternoon.
And manager Paul Simpson went for two changes from the side that drew with Stockport on Tuesday with Ben Barclay and Ryan Edmondson in for Joel Senior and Jordan Gibson.
That brought a change of formation to a 4-3-3 line-up with the away team looking for the points to keep their automatic promotion dreams alive.
It was a tight start, with both teams trying to get the football going, and it was United who had the first chance of the day when Moxon let fly from 22-yards. It took two deflections, but Gordon was stopped in his tracks by the referee's whistle.
Barrow thought they'd scored on nine minutes when an overlap brought a cross from Newby and a flick from McClelland. Neal had the width of the target to aim at but Holy was alert and he dived to make a two-handed save as the header arrowed at his nets.
There was a corner for the visitors when Moxon threaded a pass through for John-Kymani Gordon to chase. Newby went for safety first, but it proved to be a key moment as Moxon sent the set piece to the front stick. Dennis flicked it on, and Barclay stuck to the task as he stabbed at it twice before backheeling it over the line following an almighty scramble.
The Bluebirds had a scramble of their own at the other end when Gotts scissor kicked a corner back into the mix. Huntington got in the way as Ray threw a boot at it. Holy was relieved to see it spin past his upright.
Josh Gordon was next to have an effort blocked as he found space, and Holy stayed calm to pull the spinning ball into his chest.
A neat move from the white shirts saw Gotts find Whitfield in the hole in front of the defence as the game ticked along at a decent pace. Once again it was easy for Holy to claim.
Carlisle were incisive after a long delay to the game as McClelland received treatment, with Moxon surging in from the left to feed it to Guy. His shot was stopped, but that invited Barclay to cross. Armer sprinted in to get on the end of it but his header was smothered by the recovered McClelland, who survived the appeals that followed for handball.
John Kymani-Gordon rattled a wild shot into the stands after he'd used pace to get to the edge of the box, and Edmondson was thwarted by a thigh after two deft touches had sent him into a dangerous area on the angle.
A carbon copy of the earlier burst from John Kymani-Gordon put him on the 18-yard line once again, but his low bullet was diverted for a corner on this occasion.
An unbelievable sliding tackle from Armer was possibly the moment of the first half after Whelan had gone to ground. Whitfield exploited the gap, but the left back was perfect with his timing as he dealt with it with his toe before a shot could be fashioned.
Moxon spotted John Kymani-Gordon on his own deep into time added on but the connection from the Palace loanee lacked venom and it bobbled into the side netting.
The opening exchanges of the second half stayed mainly in the midde third, but that changed when Brough ran out of his own half with the ball at his feet. Huntington got an important block to send the eventual shot for a corner. The short routine from Newby was dealt with.
A cross from the left from Brough caused a moment of panic when it was stopped by Newby eight-yards out. He couldn't set himself to finish it off and the clearance was completed.
Barrow had a real opportunity to level it up just past the hour when a whipped ball into the box left Tom White with just one player to beat. He was disappointed as he rebounded it off the defender, and Neal and Gotts were equally frustrated as they somehow conspired to send it straight at Holy, who was already on the floor, when they had the target at their mercy.
The red shirts broke, with JK Gordon instrumental in keeping possession. Dennis released Guy, and he returned the favour with a rolled pass on the edge of the area. United's top scorer fell to the floor when his shot bent too close to Farman.
Callum Guy hit the afterburners to turn defence from attack from the deep inside his own half. He left his marker in his wake, then checked back to bring Dennis into play. Armer and Patrick worked hard to open things up, but JK Gordon nodded wide on the leap.
Barclay was superb at the back as he blocked and tackled to stop Newby and Gotts, and Gotts had another charged down by Whelan when the ball pinged around inside the area for what seemed like an age.
Omari Patrick was next to turn defence into attack when he skipped through three challenges to go 80-yards up the pitch. He cut back inside as he got into the area, but the block was made as he pulled the trigger.
Holy dropped to a knee and used both gloves to take the sting out of a Newby rasper from range, and he was able to watch on in comfort as Warren thrashed a poor cross high over everybody having done all of the hard work in getting up in support.
Tom White was excellent for the hosts when he got a boot to a Patrick volley in time added on at the end of the game. Armer and Patrick had bounced it off each other in the build up, with Gibson and Garner also involved.
It was good stuff from Carlisle as they managed the game out, despite a thunderbolt from Kay that smacked the post, with Farman also forward for the free kick and, with results elsewhere, it was a hugely important three points from a very solid away display.
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Goals
Carlisle United - Barclay (16)
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Bookings
Barrow - Gordon (36), Brough (57), Wild (78), Canavan (86), Farman (86)
Carlisle United - Huntington (57), Devitt (86)
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Teams
Barrow - Farman, Brough, McClelland (Warren 46), Canavan (c), Newby, Gordon, White, Neal, Gotts (Garner 84), Ray, Whitfield (Kay 78). Subs - Lillis, Taylor, Young.
Carlisle United - Holy, Barclay, Whelan, Huntington (c), Armer, Moxon, Guy (Devitt 85), Mellish (McCalmont 84), Gordon (Garner 70), Dennis (Gibson 70), Edmondson (Patrick 64). Subs - Kelly (gk), Robinson.
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Match officials
Referee - James Bell
Assistant Referee 1 - Philip Dermott
Assistant Referee 2 - Mark Dwyer
Fourth Official - Martin Woods
Observer - Gary Kellett
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Attendance - 4,515 (640)