Fleetwood Town 1 Carlisle Utd 2: Carlisle’s luck turned here last night, but there was nothing fortunate about the way they won this game. There won’t be a more emphatic goal all season than the one Tom Miller sank into Fleetwood’s net to settle this Carabao Cup first round tie.

The defender had come on to try and protect Carlisle’s lead at the Highbury Stadium. When that mission failed, and extra-time was forced, Miller went into the home side’s box to power home a Danny Grainger corner.

With his namesake Shaun having earlier scored, before Jordy Hiwula’s leveller, Carlisle set about this game against League One opposition with good intent. They earned their place in round two – and fortune also favoured them. The winner of the half-time draw, in a crowd of 1,711, was the Blues’ chief executive, Nigel Clibbens.

He gave that cash to the travelling fans, but the win United donated could be even more valuable if they land a big fish in Thursday night’s draw. Keith Curle has not disguised the importance of extra cash at these tight times and at least one cup run in 2017/18 would be extremely welcome.

So would progress in the league, of course, and players like Richie Bennett and both Millers presented their case here for starts at Cambridge. The former Barrow man (Bennett) caught the eye with some old-fashioned target-man play that went down well with United’s 571 travelling fans, while Miller was alert to his partner's work in a fine individual display.

Before kick-off one was tempted to ask if the EFL’s latest rule change had come at the worst possible time for Carlisle. An extra substitute allowed in extra-time? Come back when we’ve got a fully-fit squad, Mr Harvey.

First, though, it was hoped Carlisle’s players could negotiate the difficult-looking tie in normal time, and be more potent than on the opening League Two day against Swindon.

Bennett, whose height and presence had also caused the Robins a few problems, was included from the off here, with pre-season’s leading marksman Miller also in for a start he must have felt was merited.

The most welcome news, though, was Tom Parkes’ inclusion, just three days after a jarred ankle had seemed to shred Carlisle’s defensive numbers down to the marrow. Also at the back: a first start since January for Mark Ellis, as Miller (T) dropped to the bench with Hallam Hope and Nicky Adams.

In the red corner, meanwhile, Kyle Dempsey began as a substitute against his former club.

For Fleetwood the aim was a second-round place for the first time; for United, the chance of a money-spinning run which was sorely needed. Carlisle have generally fronted up well in this competition under Curle and showed their appetite early on, when Ellis’ first sliding challenge brought applause from the travelling fans while, upfield, Bennett was eager to engage Uwe Rosler’s centre-halves in physical battle.

The summer signing appeared a focal point for Carlisle’s ventures upfield, which came as their defence kept Fleetwood’s passing game in front of them. The hosts switched the ball sharply in the opening stages but United’s tactic of bringing their wide men (Jamie Devitt and Reggie Lambe) infield helped them outnumber the hosts as things went on.

The nature of the Blues as a work in progress was evident as Curle and Simon Tracey barked continued positional orders at Bennett as United prepared to launch a set-piece. Otherwise, though, there was some impressive work from the team in blue. With Mike Jones often dictating the direction of play, a quick passing move released Devitt to test Alex Cairns with a dipping shot. Lewie Coyle volleyed Joe Maguire’s cross wide for Fleetwood, but Carlisle had steadily built a useful spell in the home half – and from it came the opener.

Again, they aimed for Bennett, and were quickly onto the second ball as Fleetwood battled it away. Lambe sent Miller scampering behind the defence to the left and with some smart movement the striker came back inside and his shot looped over Cairns, helped by a deflection.

This was more inventive than United had been in the corresponding half against Swindon, and it also gave them something to defend. In response, Coyle was quick when attacking space down Fleetwood’s right, evading Jones and Grainger, but Jack Bonham got down well.

Minutes later, the keeper smothered a Hiwula shot that had lost its sting through a block. Ellis, next, was in the way of Ashley Hunter’s shot as he attacked Devante Cole’s cross.

Fleetwood seemed capable of opening Carlisle up but did not yet look razor-sharp. The half ended with Rosler appearing frustrated as balls forward failed to connect with Cole or Coyle. Only once did they truly scare United, when Hunter let fly from 25 yards – but Bonham excelled with a flying save.

It was a suitably defiant end to a gutsy half, and should have been rewarded with a second Blues goal. Just three minutes after the restart there was a commanding jump by Bennett and a flick which put Miller away. He slotted it inside to give Lambe the perfect chance – but Cairns saved the Bermudan’s shot.

One wondered if, at some stage, the League One team would make United regret passing up such a chance. At first, though, Carlisle kept pushing Fleetwood, Bennett’s target-man play increasingly bothering the hosts. His next leap again found Miller, but when Devitt then went over in the box, Carlisle’s penalty appeals were ignored by Salisbury.

Rosler then sent Dempsey on – along with Conor McAleny – to see if the young Cumbrian could turn things. Dempsey got a warm reception from the travelling supporters, and then the ball in the face from Joyce as Fleetwood bounced back at Carlisle.

The pace of the hosts’ attempted comeback duly increased. McAleny fed Hiwula from the left but a strong block denied the midfielder. Curle responded by removing his goalscorer and sending on the other Miller; Tom going to right-back and Liddle stepping into deep midfield.

This officially put United on the defensive as they tried to keep Fleetwood out. Maguire curled over a free-kick, but the hosts’ next attack was more precise, as a probing ball down the right was perfect for Coyle, and his cross was stroked home by the arriving Hiwula.

Carlisle’s lead was over and so was Bennett’s hard-working night, as Hope came on for the final 20. Fleetwood’s pressure continued and almost broke United when Bonham spilled a deep cross but Hiwula couldn’t turn it home.

Carlisle tried to reply through Hope’s running and Devitt’s craft, but the hosts were noticeably better for Dempsey’s passing and McAleny’s intent. United did stage an injury-time flurry which saw Ellis go close at a free-kick and Sam Cosgrove on for his debut, but neither side could prevent extra-time.

The additional 30 minutes then saw a small piece of history, as Rosler brought on a fourth sub – allowed under new competition rules – Wes Burns replacing Hiwula. McAleny, though, was the greater threat, twice going close.

But then Carlisle struck again, and how. Grainger curled a corner into the heart of Fleetwood’s box from the right, and Tom Miller rose to bury an unstoppable header, hurting himself in the process.

He was fine after treatment, as Harvey Rodgers then saw red for the hosts after a skirmish in the box. Extra pain for Fleetwood, as United went dramatically through.