Just 14 seconds were on the clock when Kuffour opened the scoring and that lead was doubled in the 13thminute when Hause headed home at the far post.
Izale McLeod reduced the deficit five minutes into the second half, but the two-goal cushion was restored in the 78th minute when skipper Stuart Lewis drilled into the bottom corner.
Blues weren’t finished yet though, and Morgan capped off an excellent all-round performance when he curled into the far corner with six minutes remaining.
Ainsworth made five changes to the side that secured a late point against Scunthorpe last time out with four of those alterations forced on Blues’ boss.
Leon Johnson (hip), Paris Cowan-Hall (knee), Steven Craig (thigh) and the suspended Josh Scowen were all unavailable, while Matt McClure was named on the bench.
Marvin McCoy, Matt Bloomfield, Max Kretzschmar, Dean Morgan and Jo Kuffour were the men to come in, while there were appearances on the bench for Sebastian Cann-Svard and Lee Angol, the latter’s last appearance for the Wanderers coming some 15 months ago.
The swirling wind was in Wycombe’s favour in the first half and Ainsworth’s men made the most of that advantage within 14 seconds when Kuffour drilled an unstoppable effort past Matt Duke. The striker received the ball just inside the area from Arnold before making space for himself and powerfully finding the bottom corner.
Duke prevented a second 60 seconds later by saving well from Dean Morgan, before being called into action again in the fifth minute when he did well to parry Kretzschmar’s daisy-cutter away for a corner.
Morgan thought he had doubled the advantage in the eighth minute when he headed home from eight yards, but his celebrations were cut short as the assistant referee had raised his flag for offside.
Wanderers were playing some excellent football early on and had adapted far better than their hosts to the difficult playing conditions, and Bloomfield’s deflected strike had Duke scrambling across his goal before drifting wide.
From the resulting corner – in the 13th minute – Kretzschmar picked out Morgan who headed back across goal for Hause to head in at the far post and give the Blues a second goal that their early play had fully deserved.
It was almost three in the 17th minute when Kuffour was played in on goal, but Duke was well positioned and rushed off his line to get just enough on the striker’s shot to turn it away for a corner.
McCoy to well to head away former Wanderer Chris Hackett’s dangerous cross at the far post in the 21st minute as the home side launched their first real attack,
Norhampton were forced into their first change after 21 minutes with Ian Morris limping off and boss Aidy Boothroyd had seen enough six minutes when he made his second change, replacing the ineffective Clive Platt with Roy O’Donovan.
The hosts started to come back into the contest midway through the half and Ingram was called into action for the first time on the half hour as he parried away Izale McLeod’s stinging drive before claiming the rebound.
Kuffour was just unable reach Stuart Lewis’ intended through ball as both he and Kretzschmar broke at pace, before Wood fired wide from fully 35 yards after winning the ball back near the halfway line.
The Cobblers should have reduced the deficit four minutes before the break when O’Donovan’s initial shot fell to McLeod six yards out, but he inexplicably fired over with the whole goal to aim at.
O’Donovan was perhaps lucky to stay on the pitch in first-half injury-time as he appeared to swing an arm in the direction of Hause, who went down holding his face. However, referee Simon Hooper awarded Wanderers just a free-kick.
Half-time: Northampton 0-2 Chairboys
Boothroyd made his final change at the start of the second half with Luke Norris replacing Reid, who already been booked for a foul on Morgan.
With the wind now in their favour, the Cobblers were quick out of the traps and McCoy did well not turn Hackett’s cross into his own goal before the ball was recycled and Norris acrobatically fired inches wide of Ingram’s right-hand post.
Their vastly-improved performance was rewarded five minutes after the restart when McLeod prodded home from close-range after a scramble in the Wycombe penalty area.
Wanderers responded well and Kretzschmar’s 25-yard free-kick landed on the roof of the net with Duke struggling after deflecting off the top of the wall.
Morgan forced Duke into a fine stop in the 57th minute when he dived to meet Wood’s free-kick from the left, only for the Northampton keeper to get a fingertip on his effort.
McLeod sliced harmlessly wide from inside the area and both teams were creating chances with the wind not helping either defence.
Stewart produced a fine last-ditch challenge to deny Norris, who looked like he had broken through on goal in the 66th minute and Northampton were dealt another blow before play resumed as Mathias Kouo-Doumbe limped off after what looked like a hamstring injury. This forced thehosts to play the remaining 23 minutes with 10 men as they had already used all their allotted changes.
Ainsworth made his first alteration 20 minutes from time with Billy Knott replacing Kretzschmar and Knott had a hand in Blues’ third eight minutes later. The midfielder cleverly found space on the left hand-edge of the area and his cut-back was perfect for the on-rushing Lewis who made no mistake and drilled low past Duke first-time from inside the area.
It was almost four 60 seconds later when a ball over the top caught out a static Northampton defence and Arnold’s controlled first-time effort was just tipped over by Duke.
Wycombe didn’t have to wait long for a fourth though as it came with six minutes remaining. Morgan did expertly well to make room for himself in the area and delicately curled past the despairing Duke and into the far corner from 12 yards.
Kuffour came off to a standing ovation in injury-time with McClure his replacement and Wanderers went in search of a fifth, but the loud 439 vocal following ultimately had to make do with just a fantastic four!
Wanderers: Ingram, McCoy, Wood, Stewart, Hause, Arnold, Lewis (c), Bloomfield, Kretzschmar (Knott 70), Kuffour, Morgan.
Subs: Horlock, Cann-Svard, Spring, Angol, Morias, McClure.
Northampton:Duke, Amankwaah, Widdowson, Reid (Norris 46), Kouo-Doumbe, Hackett, Ravenhill, Morris (Demontagnac 22), Dallas, Platt (O’Donovan 27), McLeod.
Subs: McNamara, Emerton, Collins, Deegan.
Attendance: 4,353 (439 Wycombe)