United had a sell-out away allocation for their trip to Victoria Park - a first meeting between the clubs for three seasons following Hartlepool's return to the Football League this year.
Boss Chris Beech made two changes to the starters for the first time in five league games with Clough and Feeney stepping up as Alessandra and Dickenson moved onto the bench.
Hartlepool, who have had a good start to life back in League Two, were unchanged as they looked to continue their good home form.
The away side started well with Riley and Tanner keeping the ball on the halfway line. It was popped forward to Abrahams and he used Clough before spreading it to Armer. His cross was charged down.
There was a yellow card for Clough when he put the ball in the back of the net from an Abrahams cross. The visiting cheers were quickly dampened when it came to light that a raised hand had been used.
Balls from wide have been a theme of the Pools season so far and Francis-Angol sent one in on seven minutes for Goodwin to attack. The header had power but it was always high.
Pools took the lead on 13 minutes when a deep cross was initially cut out by Tanner. His first contact went high, and Ferguson pounced to nick it off his toes before he could clear. A pass inside for Goodwin brought a cushioned lay-off, and Burey made no mistake as he swept a curler into the top corner from 16-yards out.
United worked hard as they looked to settle, but Feeney was needed when Burey dropped a shoulder to step into the box from the right flank. His low drive was going in until the defender got in the way.
Long throws from Riley caused problems at the other end as Feeney and McDonald challenged, and a half clearance from one launch on the half hour fell for Armer to nod. He looked for Clough, but Killip was quickly off his line to grasp it.
It was a half of few clear chances, with the teams battling hard to keep it tight, but Burey opened space for Sterry to deliver as he overlapped by the right hand touchline. The ball fizzed across the face of goal and Goodwin was wasteful as he guided a volley wide of the mark.
That proved to be a costly miss as the visitors sprung forward on the attack almost immediately. Armer beat his man and whisked it in, and Zach Clough opened his account on his first start for the club with an excellently measured finish.
United came again when Mellish got busy across the back line. He found Tanner, who sent one deep, and Armer was first to it with a nod on the rise. Mellish was ready to shoot until the flag went up.
An early corner after the break from the hosts saw Norman impeded as he tried to catch it, but the referee was there to see it before any profit could be made.
Riley tried to pick a perfect pass in response when he took control of a short throw from Armer. It was angled for Tanner to chase, but the keeper ushered it out of play.
It was tight, with absoutely no room to move or loiter on the ball, and it wasn't until Riley threw long on 64 minutes that another chance was created. Clough had a go at an overhead kick when it came his way, and the follow up cross from Abrahams had to be nodded behind.
Pools responded with a floated free kick from deep which brought blocks from McDonald and Feeney as Featherstone had a go. But the ball was quickly returned and Holohan somehow found the spot when he snapped up the loose pieces with a lob from the edge of the box that crept over the dive from Norman.
United boss Chris Beech went for a triple substitution, with Alessandra, Dickenson and Young joining the fray, but the visitors had a 25-yard free kick to contend with as they got themselves in a muddle in their own half. Ferguson got it up and over the wall but it was wide of the upright.
Great work from Young at the other end saw him wriggle his way past two challenges before crossing, but Liddle lunged to beat it away.
The Cumbrians had a real chance to level things up on 78 minutes when Guy swept a set piece from wide into the mix. Whelan was surprised when it made it to him, and a hurried header bent high and landed on the roof of the net.
Hartlepool closed ranks as the clock ticked down, and Brad Young was disappointed when he snatched at one in time added on. He came under pressure from two defenders just as he shaped to shoot and the effort was pulled past the post.
McDonald was sent forward to bolster the attack, and a flick from a throw almost the did trick. Sterry got there before Whelan could touch it.
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Goals
Hartlepool United - Burey (13), Holohan (69)
Carlisle United - Clough (38)
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Bookings
Hartlepool United - Liddle (87)
Carlisle United - Clough (3), Guy (68)
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Teams
Hartlepool United - Killip, Sterry, Byrne, Liddle, Francis-Angol, Ferguson, Shelton (Daly 63), Featherstone, Holohan, Burey (Ogle 82), Goodwin (Molyneux 65). Subs - Mitchell (gk), Cullen, Odusina, Smith.
Carlisle United - Norman, Tanner, Whelan, McDonald, Feeney (Dickenson 73), Armer, Riley, Guy, Mellish, Clough (Young 73), Abrahams (Alessandra 73). Subs - Jensen (gk), Devine, Mampala, Toure.
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Match officials
Referee - Andy Woolmer
Assistant Referee 1 - Sam Lewis
Assistant Referee 2 - James Wilson
Fourth Official - Conor Brown
Observer - Roy Pearson
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Attendance - 6,112 (1,000)