Jermain Defoe's 13th minute strike had appeared to set Hammers on their way to a comfortable and deserved victory as they dominated the first half, but the second division side fought back to equalise through substitute Chris Brandon just seven minutes into the second half.
Despite peppering the Chesterfield goal with shot after shot for the remainder of normal time, and throughout the 30 minutes of extra time, Hammers couldn't find the vital second goal, and memories of our spot-kick defeat at Reading at the same stage of last season's competition began to fill the air.
However, with Di Canio, Sinclair, Minto and Lomas all converting from 12 yards, Mark Allott's miss handed Carrick the chance to blast the ball home in front of the ecstatic travelling supporters.
It may not have been as smooth a passage as the first half had suggested, but the bottom line is that Hammers are now in the hat for the third round, and return to Premiership action against Birmingham City on Saturday afternoon with their high level of confidence still intact.
First Half Report
Just as they had against Chelsea on Saturday, Hammers started with a high tempo to their game and it took Di Canio only a minute to attempt a repeat of his stunning goal at Stamford Bridge, as he sent a stinging right-foot volley just inches over the bar from 20 yards out.
That set the mood for a thoroughly professional and convincing first half display, as the visitors besieged their opponents with wave after wave of flowing attacks.
After just six minutes, Cole raced on to a lofted pass from Sinclair and beat Muggleton to the ball, but his firm touch ran out of play. Sinclair then saw a far post header, drop wide of the target, before Breen sliced wide from 12 yards out following good work from Di Canio on the left.
On 13 minutes, Hammers got the predictable reward that their early efforts deserved, when Schemmel's long pass from his own half caught out the flat-footed Chesterfield defence and Defoe raced clear to stab the ball through the legs of goalkeeper Carl Muggleton from eight yards out.
The second division side hadn't conceded a goal in 576 minutes of competitive football prior to tonight's game but, as Hammers then went in search of an immediate second, it didn't seem likely that Muggleton would be waiting that long to pick the ball out of the net again.
Far from sitting back and defending their lead, Roeder's men continued to push forward and Lomas and Di Canio both saw efforts fly just wide, before Defoe missed a decent chance to grab a second on 24 minutes when he shot straight at Muggleton following a low cross from Di Canio.
Paolo then combined brilliantly with Cole, whose clever back-heel found the Italian in the six-yard box, where he twisted one way, then the other, before seeing his shot deflected wide for a corner.
It was non-stop pressure from the Hammers, who had restricted Chesterfield to just a couple of hopeful shots from the edge of the penalty area that failed to find the target, and the only mystery was that the glut of chances had produced just one goal.
The half ended on a slightly sour note for the visitors, as Di Canio was harshly booked for diving in the penalty area when it appeared he had simply lost his balance, while Schemmel was also shown a dubious yellow card for a foul on Reeves.
Half-time: Chesterfield 0 West Ham United 1.
Second Half Report
Not many Hammers fans will have paid much attention to the substitution made by Chesterfield at the start of the second half, as Martin Booty was replaced by Chris Brandon. However, David James would soon come to notice the Spireites midfielder as the hosts reacted quickly to the rollicking they had most probably faced during the interval.
Brandon gave a hint of what was to follow when he skipped down the left just two minutes after his introduction. James raced out to clear but was beaten to the ball by the 26-year-old, who thankfully couldn't prevent it from running out of play for a goal-kick.
On 52 minutes, though, his touch was more prolific. Ebdon's slide-rule pass left the Hammers defence flat-footed as Reeves ran back from an offside position and Brandon sprinted clean through on goal, committing James with a clever dummy before side-stepping the England keeper and slotting home.
It was an equaliser that simply hadn't seemed possible for Chesterfield before the break, but having no doubt realised their fortune at being let off the hook by the Hammers' wasteful finishing, Dave Rushbury's side were enjoying a renewed lease of life.
Once again, though, Hammers showed the fighting spirit that has been apparent on their travels at Tottenham and Chelsea this season, and set about trying to restore their lead.
Di Canio saw a curling free-kick drift just wide after Michael Carrick had been fouled on the edge of the area, while Minto also shot wide from a similar position and Cole had an effort deflected over for a corner.
Cole then played a delicate one-two in the area with Di Canio, only to see Muggleton smother his shot, and the Chesterfield keeper then kept his side in the competition with a string of fine saves, including a superb one-handed block from Defoe and a reflex save to keep out a left-foot effort from Carrick with just three minutes remaining.
Having grown in confidence as the game wore on, Chesterfield fought gallantly to keep their Premiership counterparts at bay and, from a side who looked hardly up for the fight in the opening 45 minutes, they now entered extra-time confident of inflicting another cup upset on the Hammers.
Score at 90 minutes: Chesterfield 1 West Ham United 1.
Extra-time report:
West Ham's Premiership level of fitness and stamina began to show as they dominated the first period of extra-time, but Chesterfield's determination and self-belief ensured that the visitors found it hard to make the all-important breakthrough.
Following Di Canio's corner, Breen saw a header cleared off the line, before Lomas volleyed the rebound wide.
Di Canio had a snap-shot well saved by Muggleton, while Cole and Carrick were both denied by last-ditch challenges as they wriggled into the penalty area.
In the second period, Cole wasted a glorious chance when he headed wide from 10 yards out after a pinpoint cross from Sinclair, while Defoe was denied space as he fought tirelessly to find a winner.
Muggleton then had the last word as he superbly tipped round a stinging low shot from Cole and, having only one goal to show for their efforts, Hammers were left to faced the dreaded penalty shoot-out…
Penalty Shoot-out (Chesterfield take first kick):
Burt - Scores
Di Canio - Scores
Ebdon - Scores
Sinclair - Scores
Allott - Misses
Minto - Scores
Hudson - Scores
Lomas - Scores
Brandon - Scores
Carrick - Scores
Full-time: Chesterfield 1 West Ham United 1 (After extra-time, West Ham win 5-4 on penalties)