Indeed, Gareth Evans' fifth-minute header had put the League Two underdogs in the driving seat before Lee Bowyer's late leveller forced extra-time against a motivated Macclesfield side, who were forced to play that final half-hour with just ten men.
Following Sunday's defeat at Manchester City, Curbishley had made five changes as George McCartney, Bowyer, Hayden Mullins, Luis Boa Morte and Freddie Sears were called into the side.
Despite eliminating Championship outfit Blackpool with an illuminating display in the first round, Keith Alexander's win-less, goalless, 91st-placed side had sadly blown a fuse with a hat-trick of defeats in their opening three matches of their League Two campaign.
And the Macclesfield manager made three switches in response to Saturday's loss at Accrington Stanley as Richard Walker, Francis Green and Shaun Brisley were named in the starting line up.
There may have been 75 league rungs separating Curbishley's men from the Macclesfield mongrels but straight from the kick-off West Ham's Premiership pedigree counted for nothing as Francis Green sent an early sizzler scorching over Robert Green's crossbar.
Then, with just five minutes on the clock, Ahmed Deen floated over the Silkmen's second corner of the game and Evans rose highest to send a powerful eight-yard header ripping into the net.
That sent shockwaves around a sparsely populated Upton Park and, as the embarrassed East Enders amongst the crowd of 10,055 came to terms with the early setback, they could only watch on aghast as the breaking Sears saw his shot turned aside by Jon Brain, who then gratefully clutched the twisting Dean Ashton's shot.
Boa Morte also sent an ambitious, angled 20-yard free-kick whistling over the crossbar before shooting meekly at Brain and then being cautioned for felling Izak Reid.
The hapless Hammers - who also lost Valon Behrami with a face injury - were labouring badly and although Ashton curled a 25-yarder onto the crossbar in the closing stages of the opening period, that still could not prevent them from departing at the interval to a deserved chorus of boos.
The Macclesfield fans were still pinching themselves as the solid Silkmen departed with that precious early lead still intact and Alexander's side emerged for the second period equally determined to protect their advantage.
As the hour mark approached, Curbishley introduced Cole and Reid at the expense of Sears and McCartney in a desperate attempt to add more cut and thrust to his sorry side.
After Calum Davenport lashed behind, the well-placed Brain was there again to smother Cole's powerful angled volley and Ashton's acrobatic overhead kick before Mullins 70th-minute screamer flew wide of both the keeper's outstretched left glove and the left post.
As the cries of "You're getting sacked in the morning" rang in Curbishley's ears, with just 15 minutes remaining, Bowyer came to his manager's rescue, when he met Julien Faubert's well-flighted cross, to finally beat Brain with a downward, six-yard header.
Despite drawing level, though, West Ham still did not have enough in the tank to avoid extra time against a Macclesfield side, whose task had become yet harder following the stoppage time dismissal of Reid for a second carbon copy lunge on his nemesis of a namesake - Kyel Reid.
That extra half-hour finally saw the tiring Silkmen unravel as the diving Cole nodded over the line after Ashton headed back Faubert's 100th-minute cross.
And then in the closing stages of the first-half of extra time the stretching debutant Hines managed to get his studs to Ashton's mis-kick and turn the ball home from close range, before Reid rounded off the scoring in the 117th minute with a fine solo run and shot.