When Albion's lightning-fast striker Jason Roberts sprinted between Gary Breen and Tomas Repka to score totally against the run of play in the 28th minute, few expected this to be the decisive goal in an open game that produced so many golden chances.
It was a difficult debut for Breen (replacing Christian Dailly) who, along with fellow central defender Repka, had problems coping with the pace of Roberts and the threat of Lee Hughes. It could have been worse, because the Baggies almost made it 2-0 in a minute, but right-back Igor Balis drove his shot inches wide of the post.
But while a defence that has now leaked nine goals in four matches still looks jittery under pressure, they could not be blamed for the lack of end product at the other end, where Albion got bodies behind the ball and forced West Ham to try their luck from distance.
In all, some 18 shots peppered Russell Hoult's goal and no-one did more to try and force the breakthrough than in-form Joe Cole, who again caught the eye, especially in the first half.
The England midfielder, operating mainly on the right but popping up everywhere in the last third of the field, might have scored a hat-trick in the first 20 minutes. He was left to rue a miscue after good work on the left by the returning Paolo Di Canio and Trevor Sinclair after 10 minutes, then held his head in disbelief as his acrobatic volley on 25 minutes was turned round the post by Hoult.
And after Albion scored from a quick breakaway through the middle, with Roberts brushing past Breen, Cole should have netted the equaliser in the 37th minute, but his weak header from just eight yards drifted agonisingly wide.
Kanoute, who had a quiet night, saw a close range effort rebound off Hoult's legs in the first minute of the second half and Hammers' poor finishing was summed up best by Michael Carrick's miskick, just six yards from goal at the Bobby Moore Stand end, after Sinclair crossed from the byeline.
Darren Moore should have added to home misery but he headed over unchallenged and then the visitors were lucky to escape when Edouard Cisse, one of the few plus points on a grim night, was denied by a deflection that took his sidefooted effort inches past the post.
David James had little to do - he had no chance with the goal - but the England keeper came to the rescue of his defence again on the hour when he made a fine double save from Roberts and Hughes to keep Hammers' hopes alive.
Referee Andy D'Urso, who had the dubious distinction of being booed by the crowd BEFORE kick-off, finally booked a Hammer when Cole mistimed an aerial challenge and caught his opponent, although Joe came off worse in the challenge and needed treatment before continuing. With ideas running out, Glenn Roeder couldn't afford to lose Cole's spark and creativity, so he opted to replace Carrick and the tiring Di Canio with subs Jermain Defoe and Steve Lomas instead on 75 minutes.
Defoe made a name for himself last season as a 'supersub' but apart from one shot that was directed straight at Hoult from an angle, he and Kanoute often found themselves receiving the ball in wide positions, where they were unable to hurt West Brom.
The fans showed their understandable frustration as they booed Hammers off at the end but we should keep in proportion one incident that will doutbless provoke sensational headlines in the morning tabloids.
It was no more than a strong verbal exchange of views - nothing physical took place - between Tomas Repka and an irate supporter before the Czech was ushered down the tunnel at the final whistle.
3 - Repka misjudges a long ball over the top, allowing Hughes to sneak in behind, but the striker's shot is too weak to trouble James.
9 - Di Canio works his magic in a tight corner to find Sinclair, who chips a ball from the far side of the penalty to the far post, where Cole is lurking. However, the England midfielder completely miskicks his volley and the ball dribbles wide.
11 - Roberts gets away from Repka on the right and fires in a dangerous low cross that sails across the face of goal and away to safety.
12 - After Di Canio is fouled on the edge of the area, the ball is squared short to Sinclair, whose powerful effort is blocked by a defender.
14 - Cole collects a half-cleared corner some 20 yards out and beats one man before firing in a dangerous low shot that flies just wide of the target.
18 - Schemmel skips on to a pass from Kanoute on the right and cuts the ball back for Cole, whose low shot from 12 yards unfortunately cannons off Carrick and is cleared for a corner.
22 - Schemmel is causing problems on the right and once again races clear before cutting back a low cross to the near post that Di Canio clips just over the bar from an acute angle.
25 - Hammers are dominating and Cole once again comes closest to opening the scoring. Di Canio's perfectly weighted pass finds Kanoute, who chips the ball back to the penalty spot, where Cole unleashes a blistering volley that Hoult superbly tips round the post.
26 - From the resulting corner, Carrick finds Cole, who finds a yard of space and curls in a low shot that Hoult is once again equal to.
28 - GOAL. The visitors silence Upton Park as they take the lead totally against the run of play. A measured pass through the middle from Wallwork appears to possess no danger to the Hammers, but the pacy Roberts races away from Breen and slips the ball past James to claim his second goal of the season.
30 - Almost immediate double disaster for the Hammers, as Roberts evades Repka's reckless challenge on the left and crosses to the far post, where wing-back Balis, in acres of space, fires a half-volley just inches wide of the post.
37 - Schemmel's deep cross from the right drops on the head of an unmarked Cole just eight yards out, but the youngster somehow guides his effort wide of the target.
Added time: 1 minute.
Half-time: West Ham United 0 West Bromwich Albion 1.
46 - Hammers come out for the second half in determined mood and almost equalise within 40 seconds of the restart. Di Canio finds Schemmel, whose deep cross is only headed up in the air by Moore. The ball bounces around in the six-yard box, before Cole's low effort is deflected to Kanoute, who can't get enough power on his toe-poke to beat Hoult.
49 - Di Canio's clever pass on the left releases Sinclair, who cuts the ball back perfectly for Carrick. However, the young midfielder misses his kick from six yards out and the ball is cleared.
50 - Substitution for West Brom, Dobie replaces Hughes.
59 - As Hammers step up the pace, Carrick's ball over the top almost releases Kanoute, but Hoult rushes out to clear, only to hit the ball straight to Cisse, whose goalbound effort from 30 yards out is deflected inches wide for a corner.
60 - The lively Roberts, who has caused Breen problems all evening, gets away from his marker again to bear down on goal, but is denied by an excellent save from James, who then proves his quality again by diving to save the follow-up from Dobie.
63 - Substitution for West Brom, Sigurdsson replaces Koumas.
68 - Cisse finds a yard of space just outside the penalty area but fires his effort high over the bar.
71 - Cole BOOKED for foul on Gregan.
76 - Double substitution for West Ham, Defoe replaces Di Canio and Lomas replaces Carrick.
82 - The Hammers are becoming desperate now, as Cole wriggles across the edge of the area but ignores the unmarked Schemmel to fire a shot over the bar.
84 - With almost his first touch of the ball, Defoe runs at the West Brom defence and fires a low shot that Hoult holds well.
86 - Substitution for West Ham, Dailly replaces Winterburn.
86 - Substitution for West Brom, Chambers replaces Roberts.
Added time: 5 minutes.
Full-time: West Ham United 0 West Bromwich Albion 1.