Curbishley has found himself under pressure early in the season
West Ham came from behind to avoid a Carling Cup embarrassment at home to League Two strugglers Macclesfield.
Macclesfield led early on when Gareth Evans headed in Ahmed Deen's corner.
Lee Bowyer headed a controversial equaliser and the Silkmen were reduced to 10 men when Izak Reid was shown a second yellow card late in normal time.
A header from substitute Carlton Cole put West Ham ahead before a Kyel Reid tap-in and a fine strike from Zavon Hines eased Alan Curbishley's worries.
The Hammers boss was booed by his own fans in the crowd of 10,055 as they struggled to break down a side floundering at the wrong end of the Football League and without a point this season.
Keith Alexander's men gave an early indication of their threat when Francis Green fizzed a long-range effort over the bar.
They grabbed the opener - and their first goal of the season - when Ahmed Deen swung over a set-piece and Evans stooped at the near post to head into the roof of the net, despite George McCartney's efforts on the line.
It got worse for Curbishley when he was forced into an early change following a head injury to Valon Behrami, who had clashed with Lee Bell.
Dean Ashton found a yard of space before the break and curled an effort against the crossbar - but it did not stop the shouts of abuse from the stands as the hosts went into the dressing room.
Curbishley sent his men out early but the visitors continued to attack and it took a clearance from Hayden Mullins to prevent a Danny Thomas cross from causing danger.
Bowyer grabbed the equaliser 15 minutes from full-time but Macclesfield claimed the ball was out of play in the build-up.
Julien Faubert was allowed to get his cross in from the right and Bowyer headed in at Jon Brain's near post.
Macclesfield's Reid was dismissed for his second bookable offence on the stroke of full-time and the Hammers went in front in the 10th minute of extra-time, with Ashton nodding back across goal and substitute Cole heading in.
Hines then tapped in at the far post after Ashton had flashed a shot across goal, before fellow youngster Reid cut in and fired a fourth from outside the box.
West Ham boss Alan Curbishley on booing from home fans: "What can I do about it apart from win games and keep going? I've had this now for a little while, I'll get on with it. I'm a big boy as I've said before.
"The disappointing thing is the players are the ones that have to go out and perform.
"The fans are brilliant when they are behind us and they have to realise the effect it has when they are not behind us. It can all change at the weekend.
"Football is a bit like this, you go through periods like this. It has happened to other managers and happened a bit last year."
Macclesfield boss Keith Alexander on the sending off: "It was a scandalous, ridiculous decision. It cost us the game.
"Our performance did not deserve the referee spoiling the game for us but you don't get those kind of decisions at places like this."
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