Di Canio's brace and a first goal of the season for Jermain Defoe capped off a magnificent performance from Glenn Roeder's men, who fought back from a goal behind to take the lead and then had to lift their spirits again following Gianfranco Zola's late equaliser.
The Hammers had started the brighter of the two sides and, just 20 seconds in, Di Canio collected a loose ball 25 yards out and fed Kanoute, who collected the ball in his stride but miscontrolled as he skipped into the area and saw the chance run away for him.
Sadly, that proved to be the Frenchman's only contribution to the afternoon, as just moments later he was left holding his thigh in agony after a heavy challenge from young defender Robert Huth midway inside the Chelsea half.
After vainly attempting to run off the injury, Fredi was forced to hobble off, to be replaced be Jermain Defoe with just over four minutes on the clock.
Despite that cruel piece of luck, however, Hammers continued their high-tempo start to the game and were much the better side for the opening 20 period. The lively Defoe immediately posed problems for Chelsea with his pace and almost created an opener after 11 minutes when he skipped past two defenders on the by-line and crossed low into the six-yard box, where Di Canio was just inches away from making contact.
Three minutes later, the visitors came even closer to taking the lead when Di Canio fed Schemmel on the right and the Frenchman's cross reached Sinclair, whose acrobatic volley was superbly palmed away by Cudicini.
Just when things appeared to be heading in the right direction for Roeder's men, though, disaster struck once again, and in controversial fashion.
After Repka had been booked for a needless foul on Hasselbaink near the halfway-line in the 20th minute, Zenden swung in a deep free-kick that was met by the head of Huth, who had slipped goal-side of Minto on the far side of the penalty area.
However, before any player could react to the loose ball, referee Dean stunned most people in the ground by blowing his whistle and pointing to the penalty spot - one can only assume for a foul by Minto on the 18-year-old German.
Minto was booked in the protestations that followed, while Steve Lomas was also shown a yellow card for kicking the ball away, and Hammers' misery was compounded further as Jimmy Floyd Hasselbaink stepped up to send David James the wrong way from 12 yards out and give the hosts an undeserved lead.
As tests of character go, it couldn't have got any tougher for the Hammers. But they responded, and in admirable style. Michael Carrick - returning to the starting line-up after a two game stint on the bench - almost equalised immediately with a low volley that took a deflection but was somehow kept out by the fist of Cudicini.
Schemmel became the fourth Hammer to go in the book for a late challenge on Gronkjaer after 34 minutes, but the visitors refused to let their spirit be broken and, five minutes before the interval, justice was done.
Di Canio's quick corner was volleyed goalwards by Sinclair, Lomas touched the ball on in the six-yard box and, as Chelsea failed to clear, Defoe pounced to stab home.
With the Hammers on top again as the first 45 minutes drew to a close, the half-time whistle was a somewhat unwelcome halt to our momentum. However, that was soon forgotten just three minutes into the second period, as a moment of sheer genius from Paolo Di Canio sent the travelling fans into ecstasy.
Taking possession 10 yards in from the touchline on the right, the Italian striker scooped the ball up with his right foot before instantly unleashing a dipping left-foot volley from 25 yards out that left Cudicini grasping at thin air as it crashed into the back of the net to give the visitors the lead.
Hammers might even have added a third minutes later, when Cole's mis-hit shot from Di Canio's corner was turned in by Gary Breen three yards out, but the Irish international was correctly flagged offside.
Chelsea expectedly fought back in search of an equaliser, but with the Hammers defence holding firm against Hasselbaink and Gudjohnsen, Carrick and Steve Lomas denying Frank Lampard and Jody Morris space in midfield and David James in menacing form whenever the rearguard was breached, the Blues were finding it hard to make the breakthrough.
Enter Gianfranco Zola. The pint-sized Italian appeared as a 63rd minute substitute for Zenden and immediately set about providing the link between midfield and attack that had been missing for Chelsea.
Just 10 minutes after Zola's arrival, Minto fouled the veteran playmaker 25 yards out and there was an air of inevitability among the Hammers fans as he stepped up to curl a trademark free-kick around the wall and past James to haul his side level.
The situation once again required a courageous response from the battle-weary Hammers, and once again they answered the call. Repka and Cole both had snap-shots tipped wide by Cudicini and it was clear that the visitors were determined to leave west London with the three points they so clearly deserved.
With six minutes remaining, that determination paid off. A free-kick into the Chelsea area wasn't dealt with by Gallas or Melchiot and Defoe's pressure saw the ball run loose to Di Canio, who swept the ball past his fellow countryman from an acute angle.
The celebrations from Paolo were typically passionate, while the orders from Roeder were typically precise, as he called upon his troops to defend with ruthlessness and replaced the Italian hero with Edouard Cisse in order to quell any further threat from Zola.
The orders were obeyed and the players held on for that much-needed first victory of the campaign. The away team dug-out almost exploded with relief as the final whistle sounded, while the victory salutes from Roeder and his players signified what will hopefully prove to be a turning point in the Hammers' campaign.