Carlisle reinforced their reputation of being a good home side with a deserved fifth win from seven Brunton Park appearances under new manager Keith Curle.
Carlisle looked up for the job and an early ball forward found Amoo with his back to goal. His spin left former-Blues defender Evan Horwood on his heels but Langmead was there to make a block.
United stayed on the front foot and a high ball from Brown was cleared on the stretch by Carter as Beck tried to get a flick. Danny Grainger raced onto the rebound and his 40-yard thunderbolt could only be parried as Duke saw it late. Amoo was in the right place but his volley crept past the upright as Beck slid in to finish it off.
Northampton responded with a slick move down the left and Banks caught United napping when he overlapped on the right hand side. A precise pass found him and he brought a fine save out of Hanford with a crisp connection which had to be tipped over the bar.
A 23 yard free kick from Carter was next to be dealt with by Hanford as the Cobblers continued to push men on, but United grabbed their deserved lead when a Dempsey free kick was put behind for a corner. He trotted across to take the set piece and Archibald-Henville did the rest when he muscled his marker out of the way and guided his header into the far corner of the net.
It was all about Carlisle and Potts was unlucky when he wrapped his boot round a volley at 22 yards. A deflection took it behind and Archibald-Henville was a whisker away from doubling his tally as he sent another header just over from the resulting corner.
Good work from Asamoah eventually brought a shot and a block as he twice kept the ball in play tight by the byline. Northampton regrouped from the goal kick and Banks tried a spectacular volley as the ball dropped out of the air from a swiped cross from Byrom.
Another sweeping move found United light at the back as a poked clearance sat up nicely for Carter. He put his laces through it but Hanford dived late to tip it over the bar.
It was a strong finish to the half from the visitors and Richards was a whisker away when his 20 yard free kick dipped just a moment too late. And the blue shirts survived vociferous appeals for a penalty when another Richards effort appeared to strike an arm as it flew through bodies in the six yard box.
The reprieve was short lived as Amoo hesitated deep into time added on. Horwood was onto it like a flash and the referee had no hesitation in pointing to the spot as a tackle from behind left the defender writhing on the floor. The prolific Marc Richards scored his tenth of the campaign from the spot.
Northampton fashioned the first chance of the second period when Banks took matter into his own hands 30-yards from goal. Hanford kept his eye on it but it was always heading high. Toney did the same as he spun on the spot with Anderson at his back. He kept it down but the keeper was well placed to gather.
United had a goal chalked off for offside when Dempsey dinked a great cross into the mix. Asamoah's celebrations were cut short as his neat touch was wiped out by the assistant's flag.
Toney brought another superb save from Hanford when he curled a 20-yard free kick round the wall and a quick release from the agile stopper took Carlisle on the attack at the other end. Amoo fed it to Asamoah and the nippy striker was unlucky as he whipped a low shot just past the post.
Carlisle regained the lead just past the hour when Amoo atoned for his first half blip with a searing run down the right flank. His low cross left it on a plate for Brad Potts and he started his celebration as he lobbed the ball over Duke from close range.
Northampton were almost gifted an equaliser when Brown ducked beneath a cross at the back post. Toney took a touch and tried to squeeze it under Hanford but Brown made immediate amends with a much needed clearance off the line.
Wide man David Amoo was suddenly enjoying himself and his crosses had Beck and Asamoah interested as he peppered the box. A cut back on 75 minutes found Asamoah in close attendance yet again but the cheers were dampened as realisation dawned that it had rattled into the side netting.
A debut for second year youth prospect Connor Hammell was followed by a dangerous moment in the Carflisle box when Hackett swung the ball in. Toney got the header but it was right at Hanford.
Duke had to be at his best to stop a Beck flick from a Grainger long throw, but it was fingernail biting time in the Carlisle box as a Richards shot deflected wide for a corner. Mohamed was left unmarked as the delivery came in but he fluffed his lines as he popped his late effort well wide of the post.
Hammell missed out on a moment of glory in time added on when he had a shot diverted wide, but it was job done for the Blues as they held on to take a very important three points.
United - Archibald-Henville (16), Potts (61)
Northampton - Richards (45+5 pen)
United - Archibald-Henville (29), Brown (35)
Northampton - Carter (16), Toney (35), Byrom (56)
Carlisle United - Hanford, Brown, Archibald-Henville, Anderson, Grainger, Amoo (Meppen-Walter 90), Sweeney, Potts, Dempsey, Asamoah (Hammell 80), Beck. Subs - Eccles, Robson, Kearns, Thirlwell, Brough.
Northampton Town - Duke, Horwood, Carter, Langmead, Richards, Tozer (D'Ath 78), Diamond, Toney, Byrom (Mohamed 66), Banks (Hackett 66), Murdoch. Subs - Snedker, Robertson, Collins, Alfei.
Referee - Mr Seb Stockbridge
Attendance - 4,421 (255 away fans)