United went into their final scheduled home fixture looking to build on their five-game unbeaten run and to at the very least consolidate their top seven position, if not improve it yet further.
There was one enforced change from the away win at Barrow with Omari Patrick in for John-Kymani Gordon, who was serving the first game of a three-match ban.
United showed first with a neat flick from Edmondson from a Barclay throw. Mellish drilled it low across the face of the area but Vassell stepped in to clear. It was recycled out to the left, with Patrick using Armer as an outlet, and Edmondson made the looped cross that followed his own. His 10-yard header dropped the wrong side of the upright.
Intricate work in midfield started with shielding from Dennis. Edmondson jumped forward to chest it for Moxon to spread play to Patrick. He got his head down and earned a corner as he crossed.
The Ammies tried to hit on the break with a direct run from Barry and he tried his luck with a rasper from distance. It was blocked, and the corner fron Mallan was flicked by Smith, who got the faintest of touches. Moxon got an important touch to send it onto the inside of the post before Hendry could apply a finish. Holy stooped low to pick it up.
Edmondson was at the heart of another Carlisle attack as he sprinted back to slide into a challenge and win the ball. Barclay clipped it back his way, and his first time pass to Dennis, with a dinked touch to Patrick, was sublime. The officials somehow gave a handball decision the wrong way.
Patrick and Dennis did the hard work to keep a long ball forward alive with some instinctive touches. Mellish was up in support and a crisp left-footed volley wasn't too far away.
Smith sent a deep free kick from Watt into the Warwick as the game maintained a steady flow, and Patrick and Moxon bamboozled the defence at the other end with a training ground corner routine. it almost came off, but the cross was stopped in its tracks.
A 33-yard free kick from Mallan was deflected for a corner, and the set piece was eventually dealt with by Dennis and Armer.
A lightning quick break from the Ammies caught United out on 23 minutes after Bolton overlapped to receive a neat through ball from Barry. He looked up and saw Hendry in support, and the forward made no mistake with a powerful strike that whipped into the bottom corner.
The lead was doubled on 28 minutes when Luke Bolton played a one-two off Hendry midway inside the United half. He got his head over the ball as he arrowed straight at the box, and a toe poke from 17-yards somehow made its way through Holy's hands and over the line.
Determination from Moxon gave the crowd a lift as he spun his way out of a tackle before crossing. Mellish trapped it, and Dennis threw a boot at it, but it spun off his instep and rose high into the air.
Carlisle stayed forward and Armer connected with his right foot as a half clearance skewed his way. It was a good spell for the home side and Moxon was next to have a pop, but he dragged it wide from distance.
Holy had to save a snapshot from Hendry just before the break, after a scuffed clearance was rifled at the nets, and there was plenty for the hosts to do as they headed up the tunnel for their team talk.
The Cumbrians went for a 3-5-2 formation for the start of the second period, with McCalmont on for Edmondson, and there was a zip about the passing as the home side looked to make an impact.
McCalmont was felled as he went on a surge, with Dennis and Moxon over the free kick, but the wall did its job.
A long throw almost did the trick as it was shaved onwards at the near post, but Vassell got in the way to prevent Patrick from applying a touch.
United worked the ball from right to left well moments later and Armer's delivery was begging to be finished off, but the red shirts got there first to make the clearance.
There was a fantastic chance fashioned for Barclay just past the hour when Moxon whisked a lovely pass into the area. The defender went for a placed volley but it whistled past the post.
United created a great opening as Robinson overlapped with 67 minutes on the clock, but the offside flag went up as the touch from Dennis grazed the outside of the post.
A first time cross from Guy then skipped up off the surface and just evaded Robinson, who had steamed in to greet it, and Guy then had a thunderbolt charged down with Carlisle throwing everything at it.
The Blues thought they were right back in it on 75 minutes when Garner put a head on a lovely cross from Robinson, but the offside flag cut the celebrations short.
But Garner wasn't to be denied two minutes later when he met a Moxon free kick with a stunning header. Cairns could do nothing as it thundered its way into the bottom corner.
There was chaos on 82 minutes when United were first awarded a penalty, when Garner was cut down by Vassell. Watt first pushed Mellish in the aftermath, and the reaction was immediate with a push in retaliation that sent the Salford man to the floor. A red card was produced.
Kris Dennis ignored the histrionics that followed to claim league goal number 20 from the spot.
The hosts were brought straight back down to earth on 88 minutes when Luke Bolton cut in from the right flank before curling an unstoppable effort into the top corner, putting the away side back in the driving seat.
Carlisle were down to nine men as nine minutes of added time was announced, with Jamie Devitt signalling that he needed treatment before leaving the field of play moments later.
Salford protected their lead as the clock ticked down and the victory was theirs at the end of a feisty encounter.
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Match Sponsor - CUFC Devon Supporters
Match Ball Sponsor - Donaldsons Furnishers
Match Ball Sponsor - Ian MacDonald and Mark Nicholson
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Goals
Carlisle United - Garner (77), Dennis (85 pen)
Salford City - Hendry (23), Bolton (28, 88)
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Bookings
Carlisle United - Guy (16), Edmondson (45), Garner (78), Dennis (86)
Salford City - Touray (52), McAleny (85)
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Teams
Carlisle United - Holy, Huntington (c), Whelan (Gibson 64), Mellish, Barclay, Moxon, Guy (Devitt 75), Armer (Robinson 64), Patrick (Garner 65), Dennis, Edmondson (McCalmont 46). Subs - Kelly (gk), Charters.
Salford City - Cairns, Touray (c), Watt, Hendry (Lund 75), Mallan (Leak 80), Mariappa, Smith, Barry (McAleny 64), Bolton, Shephard, Vassell. Subs - Bellagambi (gk), Lowe, Galbraith, Morton.
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Match officials
Referee - Sebastian Stockbridge
Assistant Referee 1 - Steven Rushton
Assistant Referee 2 - Chris Isherwood
Fourth Official - Andy Haines
Observer - James Devine
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Attendance - 10,927 (469)