The Mexican hitman, who spared Bolton's blushes in the UEFA Cup against Besiktas last Thursday evening, scored the only goal of the game to see Sam Allardyce's team progress to the next stage.
The 32-year-old headed home at the back post after a cross from Khalilou Fadiga, for his second goal in as many games.
West Ham can rightly feel aggrieved having dominated the first half, but their liveliness wore off after the resumption.
Visiting West Ham dominated the opening exchanges and in the eighth minute came close to taking the lead.
David Bellion, the on-loan Manchester United striker, weaved his way into the Bolton box, only to see his left-footed shot agonisingly fly inches over Ian Walker's crossbar.
Two minutes later the Frenchman supplied a neat ball to Teddy Sheringham, who saw his shot deflected over the bar after a timely challenge by defender Tal Ben Haim.
A minute later Bellion had another good chance to give West Ham the lead, but his shot from the edge of the penalty area was well saved by Walker.
Bellion was at the heart of everything good for West Ham and in the 22nd minute saw a fierce left-footed shot parried by Walker, before the keeper eventually snatched the ball at the second attempt to stop any further danger.
The last time these two teams met in the Carling Cup was in 1994, it was the year when Bolton reached the final.
But Sam Allardyce made a string of changes to the side which defeated West Bromwich Albion 2-0 in the Premiership on Sunday.
It showed as a sluggish Bolton failed to carve out any decent chance until the 44th minute when Ricardo Gardner found himself with time and space, unmarked at the back post.
But the striker took too long over his shot and the West Ham defence cleared the danger.
Earlier, West Ham's Paul Konchesky saw a left-foot free-kick charged down and then from the rebound, fired a right-footed shot wide of the target.
A minute later Abdoulaye Diagne-Faye made a crunching tackle on Sheringham, after Hayden Mullins had provided a deft flick to set the veteran striker free inside Bolton's box.
Two minutes before half-time Bellion pulled the ball back to Marlon Harewood, but his shot was blocked by Radhi Jaidi and Diagne-Faye.
James Collins also went close for the visitors, but his header went wide of the target just before the break.
Bolton started the brighter of the two sides after the interval and Fadiga saw a powerful left-footed shot saved well at the near post by Hammers keeper Shaka Hislop.
But a minute later Bolton were in front, this time Fadiga crossing for Borgetti to head home under pressure at the far post.
Konchesky saw a curling left-footed free-kick superbly tipped over the bar by Walker, while at the other end Bolton skipper Kevin Nolan should have made it 2-0 to the home side, but he headed over from close range.
Second-half substitute Henrik Pedersen fired high and wide in the 72nd minute, before West Ham nearly levelled.
Hislop's long goal-kick found substitute Jeremie Aliadiere, but the on-loan Arsenal striker saw his shot saved by Walker with his legs.
Try as they might, West Ham could just not find a way through and Bolton nearly doubled their advantage ten minutes before time when Gardner shot wide of the target with just Hislop to beat.
Goalscorer Borgetti really should have made it 2-0 in injury time, but the centre-forward fired wide from close range. Luckily his earlier effort was enough to seal Bolton's safe passage into the fourth round.