Blatter had claimed before the game that an Albion official told him the club selected weak teams against Arsenal, Chelsea, Manchester United and Liverpool because they felt they were games they could not win.
If that was the case then Carter had not read the script as his stunning 76th minute volley - his first goal since his £1.5million summer move from Birmingham City - earned Albion only their second win of the season.
It breathed new life into their season after taking just one point from their previous six games.
The win was all the more creditable as they had to come from behind after Philippe Senderos fired Arsenal ahead with his first goal for the club, only to then gift Albion's equaliser to the former Gunners striker Kanu.
Arsenal are still searching for their first away win of the campaign and they will be wondering how they left The Hawthorns empty handed.
They dominated the game in terms of possession but could not find a way past the inspired Albion goalkeeper Chris Kirkland.
Kirkland, who was on the bench for England against Austria and Poland, was at his best in the second-half when Arsenal laid siege to the home goal.
He tipped away a low drive by Kolo Toure, twice denied Jose Antonio Reyes and then frustrated Cesc Fabregas.
The value of his heroics became clear 14 minutes from time when Carter struck with his thunderbolt.
He capitalised when the ball ran into his path after Arsenal full-back Lauren had challenged Diomansy Kamara. The ball sat-up invitingly for Carter whose first-time volley whistled past Jens Lehmann to sentence Arsenal to more away day misery.
Arsenal, who were without Thierry Henry, Ashley Cole, Sol Campbell, Robin van Persie, Gilberto Silva and Alexander Hleb, made light of having to field a weakened side as they took control of the match in the opening stages.
It was no real surprise when a spell of concerted pressure saw Senderos muscle the Gunners ahead in the 17th minute.
Albion had had a lucky escape only 60 seconds earlier after Dennis Bergkamp, skipper on his 400th appearance for Arsenal, saw his drive deflected over the bar by a last-ditch block from left-back Paul Robinson.
But the Baggies' salvation did not last long as from the resulting corner Reyes whipped in an in-swinging cross to the far post. Senderos was being marked by Curtis Davies but he simply muscled his way past Albion's new £3million central defender to bundle the ball home at the far post.
It should have been the signal for a goal avalanche from Arsenal and that could easily have turned out to be the case as Bergkamp and Robert Pires were denied by smart saves from Kirkland and Freddie Ljungberg dragged his shot wide when well placed.
Having successfully managed to avoid falling further behind, Albion managed to battle their way back into the game and were rewarded for their determination when Kanu fired them back on to level terms seven minutes before half-time.
Senderos inadvertently played a part in the goal when he headed out a cross from the impressive Albion right-back Martin Albrechtsen, whose pace caused the Arsenal defence major problems.
Unfortunately for him and Arsenal, Senderos' clearance flew straight to Kanu and the former Internazionale and Ajax marksman did not need to be asked twice to fire home a first-time volley.
Man of the Match: Chris Kirkland
The on-loan Liverpool shot-stopper stood up to everything Arsenal threw at him as he stepped up his claims for an England starting role.