Defender Matthew Upson had scrambled Birmingham level, but late pressure from Bolton eventually paid off.
Goals from midfielder Mark Noble and defender Matthew Upson in each half were enough for Gianfranco Zola's men.
Cahill joins Matthew Upson and Joleon Lescott as the players vying for a place alongside skipper John Terry.
West Ham substitute Carlton Cole hit a post, before Cesc Fabregas scored a penalty after a Matthew Upson handball.
Three confirmed absentees through injury are Everton defender Joleon Lescott, Manchester City's Micah Richards and West Ham's Matthew Upson.
Gold has said that West Ham would resist any offers for the likes of Parker and defender Matthew Upson.
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Former Manchester City midfield man Elano split Wes Brown and Matthew Upson with a glorious pass and Nilmar arrived to direct a header beyond Foster.
Before the game, first team coach Wally Downes denied reports defender Matthew Upson would miss the rest of the season with an Achilles tendon injury.
Careless mistakes gifted the Netherlands two goals in a drawn friendly last month and West Ham defender Matthew Upson gave possession away in a dangerous position.
With Matthew Upson a confirmed starter in place of the injured Ledley King and suspended Jamie Carragher, Terry will have a third central defensive partner in as many games.
Nonetheless, reports continue to suggest that Zola could be forced to sell his best players in January, including Rob Green, Matthew Upson, Scott Parker and Carlton Cole.
Cisse showed his increasing frustrations when his shot hit Matthew Upson's hand, but it would have been asking a lot for Dean to have given a penalty.
The Hammers' day started badly before they had even kicked a ball, with news that key midfielder Scott Parker had failed a fitness test, along with captain Matthew Upson.
But West Ham's leveller stunned them and they soon found themselves behind when they failed to defend a corner, Matthew Upson heading back across goal for Neill to finish smartly.
James was in action again after 40 minutes, turning a shot from Vittek over the top after a mix-up between Ashley Cole and Matthew Upson had let in Slovakia's captain.
Captain Cesc Fabregas, back in the side following an injury lay-off, sealed the win from the same spot following a handball by Hammers centre-back Matthew Upson nine minutes from the end.
Reading, who have failed to win in their last three games in all competitions, continued to struggle with on-loan defender Matthew Upson booked for a foul on Roberts after 10 minutes.
Defender Matthew Upson, who came in for the suspended Jamie Carragher and made several key interventions, concurred with Capello and Gerrard that the win had everything to do with the players' spirit.
Matthew Upson missed a great chance when his header hit the post but Birmingham were unable to battle back, despite the introduction of former Brentford FA Cup hero DJ Campbell as a substitute.
BBC: SPORT | Football | Premiership | Birmingham 0-2 Arsenal
Essien rose above the Hammers defence to head Chelsea's first from a corner and their second goal owed much to good fortune as Matthew Upson's clearance hit Kalou and looped into the net.
The penalty award, given at the instigation of the linesman, was also hotly disputed with West Ham defender Matthew Upson appearing to play the ball first in a challenge on the returning Didier Drogba.
The 31-year-old was quickly replaced in the squad by Tottenham's Michael Dawson who arrived on Saturday, while Capello will likely pick Ledley King, Jamie Carragher or Matthew Upson to deputise in central defence for England.
With 14 minutes gone and the Clarets looking to build from deep, Fox spotted Nugent in space and aimed a raking up-field pass towards the striker, who nipped in ahead of Hammers defender Matthew Upson.
It was a chance initiated by a long punt from keeper Marcus Hahnemann and created by the two Kevins, as lone striker Doyle headed on to Foley who outsprinted Matthew Upson before blasting against the bar.
Freddie Sears volleyed wide after a corner was half-punched clear by Foster before a Larsson clearance hit Matthew Upson - playing at left-back - and forced Foster into a fine reaction save at his near post.
The second chance came just before the interval - from West Ham's first corner - when Matthew Upson headed the ball on and Tristan flicked the ball goalwards only for Jon Mikel Obi to clear off the line.
However, with one skilful touch Fuller turned Manuel Da Costa, leaving the Portuguese defender on his back, and as Scott Parker and Matthew Upson arrived late on the scene with weak tackles the Jamaica striker calmly drilled the ball home.
Liverpool almost put the game out of sight six minutes after the break when - with Matthew Upson off the field receiving treatment - Kuyt found Yossi Benayoun at the far post, but the former West Ham midfield man could not keep his volley down.
Matthew Upson will deputise for King and Carragher against Slovenia and is likely to partner John Terry - who was first out on the training pitch as he attempts to move on from the headlines of the last few days - in the centre of defence.
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