The Frenchman, a half-time replacement for Edouard Cisse, found the net with nine minutes remaining as he scored one of the easiest goals of his career, yet arguably the most important.
Kanoute was lurking on the goal -ine to tap in Don Hutchison's effort which had come back off an upright.
It provided the perfect start for Trevor Brooking, who has a three-match spell as caretaker to save the Hammers from the drop.
The victory was also a pick-me-up for manager Glenn Roeder who is convalescing after suffering a slight stroke.
It looked as though it would be a frustrating afternoon for Brooking as five minutes before the breakthrough Jermain Defoe saw a chance beat Peter Schmeichel only for Niclas Jensen to head off the line.
The only surprise was that it took until the 81st minute for the deadlock to be broken as both sides carved out decent goalscoring chances.
In the opening half Defoe's lob was well saved by Schmeichel, who also did well to keep out a header from Les Ferdinand.
And there was an element of fortune as Ferdinand charged down Schmeichel's clearance only to roll his shot into the sidenetting.
City also had their moments with David James thwarting Nicolas Anelka and he was then beaten, but Rufus Brevett cleared off the line, while Shaun Wright-Phillips and Robbie Fowler also went close.
The Hammers suffered a blow early in the second half when Ferdinand was taken from the field on a stretcher with a suspected broken right leg after colliding with Schmeichel.
James made a vital save at the feet of Anelka with appeals for a penalty waved aside by referee Rob Styles.
With time running out it begun to look as though the Hammers hopes of staying up would all but disappear.
Kanoute, who has spent much of the season sidelined through injury, came to the rescue though it was a nervous finish as there were six minutes of added time due to the long stoppage to treat Ferdinand.