United headed to Harrogate knowing that the Sulphurites were looking to get back on track following a sticky run of results.
Manager Paul Simpson was forced to make one change - that was Corey Whelan back in for the suspended Jon Mellish - but there were three other switches as he kept the busy run of fixtures in mind.
Fin Back, Kris Dennis and Ryan Edmondson were into the starting XI at the expense of Jack Ellis, Jordan Gibson and Tobi Sho-Silva.
Harrogate had the first chance of the night on two minutes when the ball got stuck under Huntington's feet deep inside his own half. It came to Daly and he drilled it through bodies from the edge of the area. Holy parried and the loose pieces were shepherded away.
United crafted an attack of their own thanks to strength from Edmondson. He got to his feet after he'd been knocked to the floor, with the referee playing the advantage, and Dennis was there to help. The attempted return pass was cut out by Burrell.
The home side got forward in numbers in what was a good spell for them with Muldoon in space on the right. A low cross took a touch off Whelan and that was enough to take Armstrong, who was waiting for a tap-in, out of the equation.
Carlisle edged into the lead with 12 minutes on the ticker as Edmondson and Dennis worked a pass from a throw-in to Charters. He netted his first league goal in style, with a beauty of a 28-yard left-footed strike that literally flew into the top corner.
The Sulphurites should have been back on level terms alnost immediately, after Armstrong had broken the lines to get onto a neat pass. His cut back came to Grant, who had the width of the target at his mercy. He lost his footing as he took the shot and his frustration at wasting the moment was visible.
There was more danger as Daly twisted and turned as he found a gap in the middle of the park. He let fly from distance but Holy was equal to it.
Determination from Edmondson earned his side a corner after Armer had sent one long, and that had the away fans off their seats as Guy latched onto the clearance. He stepped into the area, curled it low, and Whelan was an inch away with a volley from eight yards that whisked just past the upright.
Harrogate were back on terms on 28 minutes when a sliced through ball from Muldoon brought hesitation from Holy, and his defence. Armstrong accepted the invitation and he got enough on a clipped effort to take it beyond the stranded keeper and over the line, as Feeney scampered back to try to hook it away.
Home tails were suddenly high and Armstrong plucked a high ball out of the sky before volleying with his laces. The keeper was beaten but it was always going wide.
Unted were on the break when Feeney showed poise on the halfway line. A weighted pass had Edmondson on the shoulder of the last man, and he checked back to feed Dennis for the shot. A block made the save easy for Jameson to make.
Holy was excellent after an incisive move down the attacking left saw Muldoon and Armstrong link again. The striker thought he'd bagged his second of the night but the stopper stayed big to both trap then smother the rasping shot.
The visiting goal lived a charmed life on the stroke of half time as possession was overturned in a dangerous area. Muldoon sidefooted it to Daly and he met that with a crisp connection. It smacked the base of the woodwork and bounced back into the box, and it was eventually lofted out of the area.
Jordan Gibson was on for Corey Whelan at the start of the second period, with a switch to a back four as Carlisle looked to stem the flow of chances, and it worked well with a great goal that started with a Back tackle that sent Moxon on a long run.
He found Gibson, but the wide man's initial delivery was cleared. Moxon recycled it and Armer called for it when he pulled into space on the left. His cross was wonderful, and Edmondson marked his return to the fold with a thundering header from close range right in front of the delighted away fans.
The hosts threw men forward but they found it harder to find a way through, with Fin Back epitomising the attitude when he slid in to get in the way of Headley after Daly and Muldoon had opened a path.
Holy had to palm a fierce dipper from a tight angle over the bar after Grant had steamed in from the left, but it was a short reprieve as Warren Burrell made the Grant corner his own. His header was impossible to stop.
Harrogate came again moments later and Austerfield swept a crunching 19-yard swirler a millimetre past the nets, with Holy a mere spectator.
Charters did the same as United moved forward, and Edmondson and Gibson kept it moving as they approached the edge of the area. The punt had Jameson beaten but it nestled in the side netting.
It was end to end as both teams looked for the fifth goal, with break met by counter break, and there was a double substitution from the away team as Sho-Silva and Harris came on for Dennis and Charters.
Edmondson showed fleet of foot when Guy sent it his way and his turn left Armer as an option. He arrowed it at the front stick but Edmondson's touch was diverted behind.
The hosts took the lead on 76 minutes when the waves parted as Headley untidily battled through a challenge. He was falling as he sent his boot through it, 20-yards out, and Holy could only watch as it bulged his bottom corner.
It was the Cumbrians now looking for a response and Back pumped a high one into a packed box. Jameson got his fingers to it before Edmondson could finish it off.
Another deep cross from Back brought a touch across the face of the target from Armer, but that was ushered behind. Huntington leaped to meet the Moxon corner, but Jameson saw enough of it to help it over the bar.
Edmondson was the width of a hair away with an instinctive volley after Gibson had centred from wide, and Holy had to dive to save two-handed from Headley as the game remained wide open.
There were loud appeals for handball when Feeney nodded a corner against Mattock in time added on, and Feeney thought he'd levelled when he sent a header over from close range after a run of set pieces came to an end. It also went just an inch too high.
But the late pressure was made to count in the last minute of stoppage time when another great corner was kept alive. Feeney had a go, Back crossed, and Moxon kept his eye on it to slam it away and earn his team the point.
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Goals
Harrogate Town - Armstrong (28), Burrell (60), Headley (76)
Carlisle United - Charters (12), Edmondson (49), Moxon (90)
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Bookings
Carlisle United - Edmondson (42)
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Teams
Harrogate Town - Jameson, Mattock, Falkingham (c), Burrell, Grant (McArdle 80), Headley, Austerfield, Muldoon, Ramsay, Daly, Armstrong. Subs - Oxley (gk), Welch-Hayes, Coley, Folarin, Frost, Horbury.
Carlisle United - Holy, Feeney (c), Huntington, Whelan (Gibson 46), Back, Guy, Moxon, Armer, Edmondson, Dennis (Sho-Silva 70), Charters (Hayden 70). Subs - Kelly (gk), Hilton, Ellis, Idehen.
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Match officials
Referee - Thomas Kirk
Assistant Referee 1 - Nik Barnard
Assistant Referee 2 - Wayne Grunnill
Fourth Official - Andy Haines
Observer - Colin Webster
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Attendance - 2,147 (599)