Koumas' first-half strike ended Norwich's four-game unbeaten run away from home and it also earned Albion an instant return to winning ways after they had surrendered their 100 per cent home record to fellow high-flyers Sheffield United in their previous game.
The margin of their victory should have been greater after a dominant first-half display, but Albion boss Gary Megson was still pleased with the three points and he said: "In the end I have got to be thankful for the way we defended.
"Norwich only got in one real shot and Russell Hoult pulled off a great save."
Canaries manager Nigel Worthington was disappointed with his side's display as they only came to life in the second-half and he said: "We will play a lot worse than that and win games.
"I was pleased with the display but disappointed with the result. We were unlucky not to get a point."
Albion should really have put the result beyond doubt by half time but all they had to show for their domination was the classy strike from Koumas ten minutes before the interval.
Strikers Scott Dobie and Rob Hulse both failed to hit the target from close range with headers, while City keeper Robert Green comfortably dealt with long-range strikes from Ronnie Wallwork and Koumas.
A last ditch challenge by City central defender Malky Mackay after 27 minutes then denied Dobie from close range.
Squandering so many chances could have proved to be costly had the visitors taken advantage of the one clear chance that came their way in the first period.
But Mark Rivers lifted his shot from six yards over the bar in the 31st minute after Craig Fleming had nodded down a corner from Kevin Harper.
Having survived such a major scare, Albion finally made their pressure pay four minutes later thanks to a piece of class from Koumas.
The former Tranmere Rovers ace was picked out on the left hand edge of the Norwich area by a pass from Wallwork and coolly curled the ball past the stranded Green.
Norwich were a vastly improved side in the second period after the introduction of Paul McVeigh and Peter Crouch.
But their comeback bid was frustrated by the Albion goalkeeper Hoult who pulled off a stunning one-handed save in the 72nd minute to turn away a goal bound shot from Fleming.