The flying Frenchman's 45th-minute winner sent a resolutely-organised Hammers up to the heady heights of eighth place while feisty Fulham were left asking themselves how they had failed to take anything out of this keenly contested riverside derby.
"We decided to come here and be dogged because that is what you've got to do when you play away in the Premiership," insisted Glenn Roeder afterwards. "As far as I'm concerned it was a good professional performance. We needed to keep it tight at the back and in midfield because we've got enough creative players in the side who can nick a goal."
Having reached 40 points and all but dispelled any niggling relegation doubts with Saturday's victory over Ipswich Town, West Ham made just one change as left back Vladimir Labant replaced the rested Nigel Winterburn in a 4-4-2 line-up that saw Joe Cole move back into central midfield alongside Michael Carrick.
Things were not so comfortable for the 13th-placed west Londoners, though, who came into this game just four points clear of the drop zone. Still firmly embroiled in the basement battle, out-of-form Fulham with just one win in the previous 11 league matches made one change, too, as Louis Saha replaced his fellow countryman Steve Marlet following their 1-1 draw at Southampton.
And after a minute's silence for HM Queen Elizabeth the Queen Mother had been impeccably observed, the concerned Cottagers then set about trying to edge themselves to Premiership safety.
Indeed, Jean Tigana's side should have got their noses in front after just seven minutes but the outstretched leg of an alert David James thwarted Barry Hayles before the supporting Sylvain Legwinski scooped the loose ball over the top from just eight yards.
A thunderous collision then saw Labant retire with a back injury midway through the half and as Hammers frantically reshuffled by bringing substitute Ian Pearce into the right back spot with Sebastien Schemmel curiously moving across to cover for the scuppered Slovakian, Saha's cross into the six-yard box narrowly avoided the sliding Steed Malbranque.
Two wayward Sean Davis efforts then threatened more danger to those taking an Easter Monday stroll on the River Thames towpath than the Hammers' goal, but with a workman-like West Ham being restricted to a series of midfield skirmishes, Edwin Van Der Sar was equally enjoying a leisurely Bank Holiday break, too.
Indeed, it was three minutes before the interval before the Dutchman was finally forced into his first save of the afternoon and even then he comfortably fielded Paolo Di Canio's tame volley to ironic home cheers.
But then right on half-time, the tide was dramatically turned when another rare Hammers' burst upfield saw Steve Lomas prod a return pass into the path of the overlapping Trevor Sinclair, whose looping by-line cross was met by the soaring Kanoute, who rose above Brevett to head home.
The story of the second period looked set to mirror that of the first as Malbranque's 49th-minute free-kick cleared the bar by inches, and then as Fulham desperately pressed for a leveller, Tigana upped the stakes with the introduction of the £11.5 million Marlet and Luis Boa Morte.
In what ultimately proved to be an inspired bid to shore up the midfield yet further, John Moncur then replaced a furious Di Canio who ended a subdued - yet toiling - afternoon by defiantly trudging some 100 yards around the pitch perimeter to watch the final quarter of the match from the tunnel.
With the tireless Cole now supporting Kanoute in attack, the England international carved out an opening for himself before curling over from 15 yards, while at the other end Cottagers' substitute Jon Harley almost found the net with his first touch, but James pulled out a superb full-length save to tip his header aside.
By now, though, the clock was ticking down on a Fulham side rapidly running short of ideas and their desperation at failing to break down that dogged and determined Hammers' defence was underlined by Van Der Sar's late charges upfield in fruitless bids to prevent frustrated Fulham from slip-sliding into 15th place.
For Glenn Roeder's men, it is now 43 points and eighth place with a game in hand over seventh placed Tottenham.
Minute-by-minute:
6 - After a quiet opening, Hayles breaks the offside trap on the right but his cross is too deep for Malbranque.
7 - Saha's clever pass finds Hayles in the area but the striker is superbly denied by the feet of James. Legwinski collects the rebound but fires his effort high over the bar.
18 - A good move involving Carrick and Di Canio almost sets Kanoute away, but the Frenchman is penalised for handball.
19 - Labant suffers a back injury in an aerial challenge with Saha and receives a couple of minutes of treatment before leaving the field for further attention.
23 - Substitution for West Ham, Pearce replaces Labant.
27 - After playing a return pass with Kanoute, Di Canio's flick almost releases Sinclair but the ball is hit with two much pace and trickles through to Van der Sar.
42 - Di Canio collects Carrick's quick throw and jinks his way into the area, but the Italian's attempted cross to Kanoute flies straight into the arms of Van der Sar.
45 - GOAL! A vital breakthrough on the stroke of half-time as Fredi Kanoute bags his tenth Premiership strike of the season. Sinclair plays a terrific one-two with Lomas and clips his cross to the far post, where the Frenchman rises superbly to head past Van der Sar into the far corner of the net. Fulham 0 West Ham United 1.
Added time: 1 minute.
Half-time: Fulham 0 West Ham United 1.
Second Half:
49 - After Repka is harshly penalised for a foul on Malbranque, the Frenchman picks himself up to send a free-kick just inches over the bar from 25 yards out.
54 - Collins whips a dangerous cross into the six yard box, but Dailly's superb defensive header denies Legwinski a strike on goal.
58 - A delightful move involving Cole and Di Canio sees Sinclair racing down the right, but his cross is too deep for Kanoute and is cleared by Brevett.
59 - Double substitution for Fulham, Marlet replaces Collins and Boa Morte replaces Saha.
63 - Malbranque's low effort from 20 yards out drags well wide of the post.
67 - Substitution for West Ham, Moncur replaces Di Canio.
71 - From Cole's deep corner, Dailly's free header flies well wide when it seemed easier for him to score.
72 - Cole runs on to Moncur's clipped pass and turns two defenders in the box but fires his shot high over the bar.
77 - Finnan booked for kicking the ball away.
79 - Substitution for Fulham, Harley replaces Davis.
80 - The Fulham sub almost has an instant impact as he nods Finnan's deep cross goalwards, only for James to superbly tip the ball round the post for a corner.
85 - Substitution for West Ham, Defoe replaces Kanoute.
86 - Cole almost breaks on to Moncur's flick over the top but is denied by a fantastic tackle from Goma.
90 - Dailly booked for time-wasting.
Added time: 3 minutes.
90 - Malbranque's corner is met by the slightly out of position Fulham keeper Van der Sar, who heads just wide of the target.
Full-time: Fulham 0 West Ham United 1.