Only Schwarzer knows why he didn't elect to clear his lines and find row Z of the East Stand when, in the 76th minute, he raced out of his area to meet a through ball from Vladimir Labant that was intended for Jermain Defoe.
Instead, the keeper only succeeded in booting the ball back to Labant whose effort from 40 yards was superbly controlled by Kanoute, who swivelled and drove a left footed half-volley into the net from the edge of the box, with Schwarzer stranded.
It was the Frenchman's only clear sight of goal all afternoon, because until then he and Defoe had been smothered by the excellent central defensive pairing of Ugo Ehiogu and Gareth Southgate, at the heart of a well organised visiting defence.
For all their second half possession, West Ham had not really looked like finding a way through the black and blue barracade.
Defoe was the only Hammer to test Schwarzer in a drab first half that was as dull as the East London sky. John Moncur and Nigel Winterburn, preferred to Labant at left wing-back as Glenn Roeder opted to start with a 3-5-2 formation, saw shots fizz wide of the post but there was little else to trouble Boro, who looked the more likely to score before the break.
Alen Boksic exploited space in behind the wing-backs - skipper Steve Lomas was given that role on the right - as Ian Pearce played his first senior game since April of last year on the right of a back three that also included Tomas Repka and Christian Dailly. Pearce, understandably, needs time to readjust to the pace of the game, although he looked more comfortable after Hammers reverted to their usual Upton Park 4-4-2 for the second half.
Roeder was forced into the switch by a knee injury to Don Hutchison just before half-time and, while Hutch had performed no better or worse than any of his team-mates, West Ham had a distinctly better shape to them once Labant moved to left midfield, in front of Winterburn, while Lomas switching inside alongside Moncur, with Cole going to right midfield and Pearce to right-back.
Labant enhanced his popularity within minutes of coming off the bench when he clattered into Paul Ince and earned a yellow card for his robust efforts. But the Slovak showed his attacking qualities on the hour when, after Cole was floored by Robbie Mustoe 25 yards out, his curling freekick brought a full stretch save from Schwarzer.
A pity for Boro that their Aussie keeper then cost his team a point they probably deserved. To add insult to injury, Ehiogu was sent off for a foul on Labant two minutes from time.
Roeder couldn't disguise his relief and delight at the final whistle. This was not a match for the purist but with playmaker Paolo Di Canio, Trevor Sinclair and Sebastien Schemmel all missing through suspension, it was an important result that lifted Hammers three places up the table.
The only disappointment were the knee injuries to Hutchison, who left the field on a stretcher, and Lomas that could sideline both players for up to a month if the early diagnosis is correct.
Minute-by-minute
3 - Ehiogu is forced to leave the field for several minutes after an accidental kick in the face from Defoe leaves him with a bloody nose.
4 - Defoe collects a ricochet off a Boro defender and advances forward before firing in a stinging shot from just outside the area that Schwarzer holds well.
6 - Moncur's quick-thinking pass releases Cole, who races past Southgate on the right and cuts the ball back, but Ince clears for a corner.
11 - Carbone's dangerous inswinging corner is flicked on by Boksic and thankfully drops just past the post for a goal kick.
13 - Kanoute receives a clever return pass from Hutchison and wriggles into the box before Ehiogu denies him with a last-gasp tackle.
14 - Moncur's rasping drive from 25 yards out sails just over the bar.
16 - After Hammers fail to clear properly, Carbone's volley on the turn is gratefully gathered by James.
19 - Kanoute's deep cross from the right finds Winterburn, who sends a measured left foot effort just wide.
22 - Middlesbrough come closest to breaking the deadlock as Queudrue outpaces Lomas and sends a low cross to the far post, where Greening ghosts past Winterburn but pokes his effort just wide.
23 - Pearce misses his attempted clearance in the box, but Whelan volleys just over.
26 - Cole booked for foul on Mustoe.
35 - Queudrue again races clear down the left and cuts the ball back for Carbone, who shoots low and wide.
41 - Hutchison is stretchered off after collapsing in agony in an off the ball incident.
41 - Substitution for West Ham, Labant replaces Hutchison.
Added time: 4 minutes
45 - Labant booked for foul on Ince.
Half-time: West Ham United 0 Middlesbrough 0.
Second Half:
54 - Stockdale booked for kicking the ball away.
55 - After Labant's cross is only half-cleared, Moncur picks up the loose ball and weaves his way into the area before firing in a shot that is blocked by a defender.
59 - Following a foul by Mustoe on Cole some 20 yards out, Labant's curling free-kick is palmed round the post by Schwarzer.
60 - Cole's long range effort is well held by Schwarzer.
61 - Ehiogu booked for deliberate handball.
62 - Greening booked for foul on Cole.
65 - Boksic's deep cross reaches Whelan, who lays the ball back to the edge of the area, where Ince is waiting to fire in a blistering shot that James superbly palms away. Whelan collects and plants the ball across the six yard box, but some brave defending from Dailly and Repka prevents Carbone from scoring.
69 - Cole bravely beats Mustoe to the ball and bursts into the area before firing a left foot shot high and wide.
70 - Kanoute's low cross is inadvertently flicked goalwards by Defoe, but the ball drops just wide of the far post.
76 - GOAL! Hammers finally make the breakthrough as Schwarzer races out to deny Defoe but only clears the ball as far as Labant, whose attempted lob from inside his own half arrows towards Kanoute, who controls brilliantly with his chest inside the area and crashes home a left foot volley from 14 yards out. West Ham United 1 Middlesbrough 0.
79 - Double substitution for Middlesbrough, Nemeth replaces Greening and Murphy replaces Whelan.
83 - Mustoe booked for foul on Lomas.
87 - Substitution for West Ham, Garcia replaces Lomas.
87 - Substitution for Middlesbrough, Windass replaces Mustoe.
88 - Ehiogu sent off for second bookable offence after foul on Labant.
88 - Ince booked for dissent.
Added time: 3 minutes.
Full time: West Ham United 1 Middlesbrough 0.