United were unchanged for a fifth consecutive game as they headed to St James Park with a six-game unbeaten run to protect.
And United were out of the blocks quickly as Mellish made a run through midfield. He used Toure who managed to feed it on for Anderton to cross, despite being fouled. The delivery from the left back was touched on by Alessandra, and Toure earned a corner as he tried to put it back into the mix.
The Blues camped forward through the early exchanges, with Tanner and Riley providing options, and the midfielder had a shot charged down as a half clearance from a Kayode throw came his way.
Exeter showed on six minutes when Williams chased down a through ball from Bowman. A shot came in from the forward as he dropped a shoulder on the angle, but Hayden got in the way to send it behind.
More defending was needed as the corner pinged around, but United stayed tight to clear their lines.
Defender Aaron Hayden survived a heavy collision with former Carlisle youth graduate Ryan Bowman, but he needed a prolonged period of treatment after a heavy fall.
United were straight back on the attack from the restart, and more dangerous forward play left Toure and Tanner with half a sight. Sparkes swung a boot to get the ball away but captain Nick Anderton was quickly onto the sliced clearance. Tom Parkes made sure the cross was dealt with as he stepped up for his team.
The Cumbrians worked hard to keep Exeter pegged back inside their own territory, and Alessandra was next to spark an attack when he spun his man on the halfway line. Toure took over, and he held it up for Riley to pull clear. A touch from the midfielder opened things up but his rasping drive was straight at Andresson.
The earlier incident involving Hayden eventually took its toll when he made a signal towards the bench, and Max Hunt was called into action to take his place. And the big centre back was immediately in action as he made a volleyed clearance from a Randall cross. Paul Farman was well placed as Law tried the same moments later.
Exeter came again, with Law having switched to the right, and his cut back was met by Collins who poked a 19-yard snapshot right at the Carlisle stopper.
United enjoyed a good spell on the half hour, and a ball over the top from Tanner found Alessandra on the run. He used Mellish, but his low delivery was chopped out before Toure could pounce.
And the visitors went close when a slick moving involving Mellish, Riley and Tanner left the latter with room to pick his pass. Alessandra got on the end of it and he was disappointed to see his glanced header spin just the wrong side of the upright.
United had plenty of ball inside the home half, and Guy almost capitalised as he found himself to be one of very few players who had stayed deep. His long range effort clipped a heel and bent away for a corner kick.
A series of visiting deliveries followed, but it wouldn't quite drop for the Blues, and McDonald completed a superb sliding clearance as the Grecians broke with Randall at the helm. The outswinging cross was primed for a Bowman strike until the defender made his timely intervention.
Determined stuff from Key saw him wind his way through two challenges moments later and he decided to go for broke as he reached the edge of the area. It had venom but he couldnt keep it down.
Guy caused trouble at the other end with a lofted corner that was met at the back stick by Hunt. The keeper flapped and got a touch as the header came at him, but he had much needed help from Parkes as they closed things down.
Deep into time added on for the first half Max Hunt sent a lovely ball down the touchline. Kayode took over, and he beat his man as he powered into the box. Toure latched onto the pass and his fizzed first-time effort from 10-yards out whisked just past the upright.
Carlisle had to be on their toes at the start of the second period when Randall surged through. He cut the ball back, but some excellent defending protected the target.
But the Grecians had the lead on 48 minutes when a Law free kick was caught on the volley by Parkes. It had made its way all the way through to the big centre half, and his swing of the boot left Farman with no chance.
A great through ball from Alessandra sent Toure on his way as United looked for a response, and he beat his man well, but it ran too far and the move was ended.
Another great away chance went begging on 57 minutes when Guy overlapped to cross on the sprint. Alessandra missed a touch, but Mellish was there to get on the end of it as he arrived late. He tried to place it, from nine yards out, but the shot lacked power and Andresson was down smartly to gather.
Gime Toure was sent off on the hour mark when he felt he'd been stood on by Jake Taylor. His reaction brought an immediate red from referee James Adcock, and the away side were reduced to ten men.
United regrouped, and Alessandra did good work to make space when he twisted away to cross. Kayode and Mellish hunted but Andresson was off his line to claim it.
Another excellent Guy free kick was cleared just as Kayode made a move, and the break that followed saw Law clip Randall into space. His cross invited Bowman to throw a boot at it, but Farman scampered out to pluck it off the grass.
Farman was needed again when a massive kick from the Exeter keeper bounced high before skipping through. Bowman wanted it, but the Carlisle glovesman judged it superbly as he used his chest and then his hands to tidy things up.
Alessandra had dropped deep, and he provided another cross for Hunt to contend with as Carlisle forged again. The header was won, but Taylor was back to assist with the work that needed to be done.
Bowman was close with a header on the jump from a Sparkes cross as Carlisle ignored the fact that they had a one-man disadvantage as they really went for it, with Reilly added to the attacking mix with just over 15 minutes left to play,
The testing Kayode long throw gave Guy a shooting chance as a launched lob was cleared his way, but he scuffed it under pressure. And the same avenue, this time from the right wing, saw McDonald recover the throw with a guided pass to Anderton. His cross was blocked, and the corner from Guy was punted away.
A goal-saving tackle from Tanner saw him get in the way after Williams had put it on a plate for Law, with United committed forward, and Patrick tried his luck at the other end after Alessandra had regained possession. The connection was crisp but it flew into the keeper's hands.
Exeter saw it through to claim their three points, and it was a disappointed group of blue shirts who left St James Park with nothing to show for their hard work.
Exeter City - Parkes (48)
Exeter City - Sparkes (53)
Carlisle United - (Toure sent off, straight red, 60)
Exeter City - Andresson, Sparkes, Law, Taylor (c), Collins, Williams, Bowman, Randall, Parkes, Sweeney, Key. Subs - Day (gk), Caprice, McArdle, Seymour, Jay, Fisher, Hartridge.
Carlisle United - Farman, Tanner, Hayden (Hunt 25), McDonald, Anderton (c), Riley (Patrick 74), Guy, Mellish (Reilly 74), Alessandra, Kayode, Toure. Subs - Dewhurst (gk), Armer, Furman, Obiero.
Referee - James Adcock
Assistant Referee 1 - Robert Dabbs
Assistant Referee 2 - Samuel Ogles
Fourth Official - Kevin Johnson
Attendance - behind closed doors