It was the home side though who had the first chance of the game in the opening minute when Frankie Simek's cross found Francois Zoko for a shot well over the top from the edge of the box. Up at the other end a Scott Arfield drive being deflected away by Tom Taiwo, with Anthony Pilkington then having a powerful cross-shot tipped over by Carlisle goalkeeper Adam Collin.
Collin again called into action moments later when he made an easy save from a long-range Arfield effort, before Ian Harte and Lee Peltier picked up a booking apiece for either side in the space of three minutes. Huddersfield then going close to scoring on 15 minutes when Rhodes beat James Chester to a loose ball down the middle only to lob his goal attempt over the advancing Collin and into the side-netting.
Five minutes later and United raced forward well on the break but skipper Paul Thirlwell wasted the opportunity as he dragged his 20-yard shot well wide. Jamie McCombe then having a looping far-post header from a Joey Gudjonsson corner easily claimed by Collin just after the half-hour mark in an end-to-end encounter.
Shortly afterwards and an Ian Harte free-kick up caused havoc in the Town penalty area, with Craig Curran's close range shot first cleared by Gary Naysmith before McCombe managed to hack Gary Madine's follow-up effort away from the line. The Terriers then breaking forward at pace as Joe Garner's low cross in saw Rhodes slide in and slam a shot inches wide of the far-post from 12 yards out.
Gudjonsson then drove an effort well wide from distance on 41 minutes before up at the other end Madine pounced on a loose ball only to bobble his half-volley from the edge of the Huddersfield box wide of the target. Pilkington then knocking a shot past the Carlisle back-stick from a Gudjonsson free-kick as the visitors had the last chance of the half.
It was the Cumbrians attacking again five minutes after the interval though when Madine had his first effort blocked by Peter Clarke, before he then dragged the rebound wide. Huddersfield though pushing forward shortly afterwards as Collin had to be particularly alert to push a pacey low Lee Peltier cross behind at his near-post.
Garner then set up Gary Roberts for a powerful half-volley well over the top as the Terriers upped the pace before it was Carlisle once more doing the work going forward barely sixty seconds later when Zoko headed a Sean McDaid cross too high and into an empty Waterworks end. James Berrett for United then setting up Taiwo for a 20-yard shot, only for it to be well blocked by Clarke.
The Cumbrians were well on top now and after 64 minutes Madine thumped a powerful low drive towards the bottom corner only to see Alex Smithies make an excellent save on his goalbound effort. Chester then moments later from a Berrett cross heading wide on the stretch in front of goal as the Blues looked to break the Carling Cup deadlock.
Midway through the half and Carlisle escaped after a Collin mistake on a clearance, Roberts crossing to the back-post where Rhodes headed against the crossbar from close range, with Garner then seeing his follow-up effort somehow cleared away over the top by McDaid. Town hitting the bar again five minutes later when Rhodes shrugged off a Chester challenge only to see his hammered 25-yard strike ping down off the underneath of the woodwork, with Harte completing the United clearance.
Madine then set up Curran for a shot on the turn which never worried the Terriers defence before Taiwo was booked on 72 minutes for a foul on Garner. Madine heading wide of the Town far-post himself from a Berrett corner before Huddersfield had a chance come and go when Rhodes could only send a scissor kick off target from a Gudjonsson cross in.
With 76 minutes on the clock Harte forced a good diving take out of Smithies with a free-kick before Harte then sent a similar effort wide of the far-post shortly afterwards. Rhodes then, from a Garner touch on, only able to drag a poorly directed shot off target. Garner involved in the game again with three minutes left when he could quite easily have been sent off for an aerial challenge on Harte, the Town striker though getting away with a yellow card.
Garner was immediately substituted by Lee Clark, but just as the tie looked to be heading for extra-time Huddersfield sent us all home early. Chester's slip to the turf down the right allowing Garner replacement Lee Novak to race away before laying the ball across the United box for Rhodes to knock the ball into an empty Carlisle net from 12 yards out. United then exiting the Carling Cup at the opening stage when they probably deserved better.