United went into their penultimate home game of the season knowing exactly what they had to do if they were to keep their play-off dreams alive.
A minimum of 10 points from the remaining four games was required, with the Blues currently sat in 11th place and five points shy of the hotly contested remaining slot.
Chris Beech made two changes to the starting line up from Tuesday night, with Nick Anderton in for the injured Rod McDonald and Ozzy Zanzala back from his niggle, to replace Omari Patrick.
Long throw specialist Dan Jones was back for the Sulphurites and he launched one early, which Stead flicked on. There was nobody there and it drifted behind.
A tumble from Stead earned the away side a free kick from the right hand angle of the area, with four minutes on the clock, and Smith was picked out by the accurate Thomson delivery. His 16-yard header sailed over the bar.
It was the visitors who appeared to have taken the lead on eight minutes when Stead slowed his run to beat the offside trap, as Muldoon clipped it through from a fortunate midfield ricochet. The big striker went round the keeper and rolled the ball into the net, but referee Chris Sarginson walked across to consult his assistant. A brief conversation was followed by the raising of the offside flag.
A huge ball over the top was challenged for by Anderton when play restarted, and Muldoon pushed through again, only to have it taken off his toe as he shaped to shoot.
But Harrogate were ahead on 11 minutes when Thomson was given space inside the area. His cross was blocked, but it spun awkwardly and Farman was out to chase it down. Jack Muldoon got there first, and his low toe poke somehow twisted its way from a very tight angle across the goal line. It hit the inside of the post and the spin took it away from Hayden and into the nets.
Stead was close to doubling the lead when a Jones delivery was guided to the back post by Falkingham. The forward couldn't wrap his boot round it and the Blues were able to clear.
The Thomson set piece caused more problems for the home team on 20 minutes when it was whisked low and hard. Stead was onto it, but his connection was weak and the moment was gone.
United showed attacking intent when Riley put a ball over the top for Zanzala to control. He took it down well, and held it up with his back to goal. Alessandra showed, but his shot as he dropped his shoulder was charged down. Guy was onto it, but he dragged his long-range effort wide of the mark.
There was more danger at the United end when Muldoon used guile to work a way between Tanner and Mellish. He opted to try his luck, but he skewed his effort into the Warwick Road End.
Carlisle crafted a bright moment when Tanner came out of his own half with the ball at his feet. He used Kayode, who stepped inside before sweeping it wide to Armer. A lobbed cross found Zanzala, and he got enough on it to send it bobbling at Alessandra, who was on the edge of the box. It wouldn't settle as it bounced high and Burrell made up the defensive yards.
Guy had two deep free kicks cleared from the area in the run-up to half time, and Harrogate broke from the second delivery as McPake showed pace. His shot on the move was deflected behind, and Thomas looked for Smith from the resulting corner. The defender met it cleanly but his header went over the crossbar.
The last action of the half was a looping free kick which was cleared only as far as Riley. He went past a challenge to make room for a thunderbolt, but another block was made before the keeper could be troubled.
United went for a triple substitution for the start of the second period with Rhys Bennett, Omari Patrick and Ethan Walker coming on for Jack Armer, Joe Riley and Lewis Alessandra.
The Sulphurites went close on 51 minutes when Thomson and Stead passed their way to the byline. A looped cross was grasped by Farman, but he was fouled just as he took it into his chest.
A long kick from the home keeper brought a corner from nothing as Burrell misjudged his header. Guy swung it in, but it stuck on the floor as Bennett got there, on the penalty spot. Kerry gratefully hooked it high.
Pace from Walker saw him carry the ball 40-yards when he latched onto a Farman throw. He went for a neat inside pass but it was just too far in front of Patrick.
Walker almost pulled the hosts level on 58 minutes when he took a pass from Guy on his instep. He feinted, then aimed at the far corner, but it took a touch off a defender and skimmed just past the upright.
It was a good spell from the Blues and play was spread to Patrick over on the right touchline. He beat his marker but a low pass was cut out.
A dipping cross from Tanner was nodded wide by Walker as Carlisle continued to probe, and Patrick had another stinger blocked when he let fly from 22-yards.
Strong defending from Anderton prevented Beck from having a clear sight of the nets with just over 15 minutes left to play, after the centre forward had controlled a driven pass from Thomson on his chest.
Carlisle were back on terms moments later when Guy sent a beauty of a free kick into the mix. Kayode got the touch it needed and it flew past Cracknell and into the top corner, making it seven for the season for the Rotherham loanee.
Beck nodded a Thomson cross straight at Farman with the game right in the balance, and Guy had another opportunity to send one in when Mellish was fouled out wide.
A deep one from Guy caused consternation as Walker then Patrick tried their luck. The rebound eventually came to Walker, but the whistle blew as Bennett and Cracknell came together.
The hosts were the width of the woodwork away from taking a late lead when Scott burst into the box from a Patrick flick. A low cross was met by Burrell, but his hurried clearance hit a sharp angle off his boot. He was relieved to see it bounce back off the bar.
United ended the game on the attack, and a Guy corner was recycled for a second delivery. Kayode flicked it but it was always heading wide.
Carlisle United - Kayode (75)
Harrogate Town - Muldoon (11)
Carlisle United - Guy (39), Armer (40)
Carlisle United - Farman, Tanner, Hayden, Anderton (c), Armer (Bennett 46), Riley (Patrick 46), Guy, Mellish, Zanzala (Scott 87), Kayode, Alessandra (Walker 46). Subs - Norman, Devine, Toure.
Harrogate Town - Cracknell, Jones, Falkingham (c), Smith, Burrell, Thomson, Stead (Beck 66), Kerry, Muldoon, Hall, McPake. Subs - Belshaw (gk), Fallowfield, Kiernan, Francis, Williams.
Referee - Christopher Sarginson
Assistant Referee 1 - Scott Williams
Assistant Referee 2 - Richard Bartlett
Fourth Official - Martin Woods
Observer - Brian Parry
Attendance - BCD