Phil Brown's men join West Ham as the only teams to have beaten Arsenal at their new ground - they had gone 17 months without a home loss - with victory also denying the Gunners a return to the top of the Barclays Premier League.
• Wenger: We're not machines
The hosts had taken the lead through Paul McShane's own goal but Geovanni struck a spectacular equaliser before Cousin headed home in the 66th minute.
"We are Hull'' sang the visiting support, as if the Premier League needed reminding. They are up to sixth and have only lost one of their first six league games.
After a frustrating opening half, Wenger may have been tempted to throw on the youngsters who served him so well in the midweek win over Sheffield United.
The Frenchman brought back his "OAPs'' who, despite their experience, still included the likes of 20-year-old Denilson and England teenager Theo Walcott.
While Wenger's Carling Cup youngsters showed no fear, the current first team were guilty of the same traits that have caused Arsenal problems in recent seasons, plenty of passing and attacking without always scoring.
With the invention of Brazilian Geovanni and the steel of George Boateng, Hull stayed within sight of Arsenal and then fought back in devastating fashion.
Cousin's presence clearly troubled William Gallas - the Arsenal skipper required treatment after an early clash of heads - but there is more to Hull's game than playing long to a targetman.
Early on, Geovanni raided down the right, then went over the crossbar with an overhead effort from the resulting corner, while Marlon King was unfortunate to be called offside when he was sent through.
It was Arsenal's cue to go through the gears but Cesc Fabregas dragged a shot wide when given plenty of time on the edge of the area.
Emmanuel Adebayor thought he had headed an opener past Boaz Myhill but Alan Wiley adjudged him to have pushed Michael Turner before climbing on McShane.
There was further desperate and brave defending when Walcott raced through, with Andy Dawson getting back to make the tackle as the teenager prepared to pull the trigger.
Walcott was presented with an even clearer opportunity when he got on the end of Emmanuel Eboue's cross but his touch betrayed him and Myhill gathered.
Brown had been furious with his players for giving away the ball and his mood did not improve when Denilson elbowed Ian Ashbee, Wiley awarding a free-kick but not booking the youngster.
Eboue drilled into the side-netting just before the interval, the closest Arsenal came to a first-half goal.
Geovanni had the ball in the net for the visitors but play had been called back for a foul long before he connected with a sweet volley over Manuel Almunia. Arsenal had been warned.
Fabregas was required to clear off the line when Boateng had an effort from the edge of the area just after the break before the hosts took the lead in the 50th minute.
Robin van Persie sent Walcott down the right, the youngster twisting and turning his way to the byline before pulling back for Adebayor. His scuffed effort went past Myhill, with McShane turning the ball into his own net under pressure from Fabregas.
Hull threatened through Dean Marney, whose scissor-kick was parried by Almunia before their reply came in the 62nd minute.
Geovanni collected the ball on the left, cut inside Walcott and let fly with a rocket into the top corner from 30 yards.
"You beauty,'' was Brown's reaction on the touchline as he punched the air.
Then Cousin scored four minutes later, getting in front of Gallas to head home from a Dawson corner.
Carlos Vela was sent on from Wenger's clutch of youngsters on the bench and he went wide after Gallas hit the bar with a header.
Myhill then tipped over from Fabregas' drive in stoppage-time as Hull clung on for a famous win.
Wenger: We're not machinesArsenal boss Arsene Wenger has demanded improvement from his players after
defeat to Hull ruined his 12th anniversary at the club.
"We had the chances to win the game,'' said Frenchman Wenger. "The commitment
was on the high side but we weren't completely switched on to the level you need
to be to win the game.
"Human beings are not machines. Perhaps subconsciously we thought we would
make it. After we went 1-0 up, we were a bit careless in not pushing on to score
the second goal.
"We don't know how costly it could be but they were committed and it was a
good lesson for us. We now know that if our attitude isn't right, we can lose
games.
"It was a bit similar to (Arsenal's match at) Fulham. You can never afford
defeats. We had a good chance to go top of the league but at the end of the day,
if we had had the same level of concentration as Hull we would have won the
game.''
Emmanuel Adebayor had an effort ruled out in the first half for pushing McShane
and Michael Turner - but Hull goalkeeper Boaz Myhill went untested for 45
minutes.
McShane bundled through his own net after Theo Walcott raided down the right
just after the break, then Geovanni's rocket levelled.
Wenger was angry with the marking for Cousin's winner, with the Gabon striker
moving across captain William Gallas from a corner to glance his header into the
far post.
It was not the way Wenger wanted to remember his 12th anniversary.
"There's nothing to celebrate, even if we had won,'' he added.
Hull manager Phil Brown was furious with his players at half-time for not
believing they could win.
After the finest result in the club's history, Brown felt he was rewarded for
his positive approach, fielding Marlon King and Cousin in attack, with Geovanni
supporting.
"We picked a team to come here and cause them problems,'' Brown said.
"We have a drive, an endeavour and a belief that we can come to places and get
a result. I was disappointed with our display in the first half when we came off
at 0-0 because I wanted to win.
"To say I was harsh in my criticism would be an understatement.
"It's one of my greatest results - Wembley and Newcastle were great but we're
proving people wrong all the time. We've got the same number of points as Derby
(achieved in all of last season) with 32 games left so it's a fantastic day!''
Hull captain Ian Ashbee told Setanta 1: "We went for it, we played with three
strikers.
"We could have come and try to shut up shop but we knew that would be
difficult against Arsenal.''
Cousin's goal was his first for Hull since joining from Rangers last month, and
the Gabon international said: "I'm happy for the team and for my first goal for
Hull. We played well together.''
Arsenal 1 - 2 Hull City
