Back came West Ham and Ilunga almost worked his way through on goal but was denied at the last by Jlloyd Samuel.
And as Bolton sat back, the hosts looked on the verge of making their dominance tell as shots came in from David di Michele and Valon Behrami.
But then in the space of four minutes, the game was turned on its head.
First, Green came out to collect a high ball but dropped it for Davies to gratefully slot home.
And then the unfortunate keeper failed to cling on to Steinsson's well-struck effort and Cahill was quickest to the loose ball to make it 2-0 to the visitors.
West Ham tried to push on and set about getting themselves back in the game, but their earlier swagger had gone and they looked stunned.
The hosts must have received a stern talking-to at half-time as they emerged after the interval with renewed fight.
And they almost halved their deficit when Cole's curler seemed to be heading for the top corner until Jussi Jaaskelainen clawed it away and on to the post.
Bolton hit back and Gavin McCann went close with a fierce strike before a Matthew Upson backpass nearly heaped more embarrassment on Green.
Interview: Gary Megson
Then, from a set-piece, West Ham gave themselves a lifeline when Upson headed back a corner for Cole to nod in, with the help of a slight deflection.
West Ham were now in the ascendancy as Bolton sat back trying to protect their lead.
But despite having much more of the ball, the Hammers were finding it impossible to break their opponents down.
Instead it was Bolton who struck again when Taylor's brilliant swerving 40-yard set-piece easily beat Green and ensured Bolton left Upton Park with all three points.
West Ham manager Gianfranco Zola: "It happens, sometimes it is the goalkeeper, sometimes it is the striker. I've missed chances from virtually the goal line.
"I'm sure Robert will come back and we'll be thanking his for saving a penalty or something.
"We have total faith in him and I have total faith in the whole team."
Bolton manager Gary Megson: "We spoke about the way West Ham would come onto us and we had to try and negate that by taking the game to them and playing in their half.
"We've got work rate, resilience and character in spades but today we played some decent football.
"To come to a club that has won its first three games of the season here, to beat them on their home patch is a big thing for us."
West Ham: Green, Faubert, Neill, Upson, Ilunga, Behrami, Parker, Noble, Di Michele (Bellamy 54), Etherington (Sears 79), Cole. Subs not used: Lastuvka, Lopez, Boa Morte, Mullins, Davenport.
Booked: Noble, Faubert, Bellamy, Parker.
Goals: Cole 69.
Bolton: Jaaskelainen, Steinsson, Andy O'Brien, Cahill, Samuel, Davies, Nolan, McCann, Muamba (JoeyO'Brien 80), Gardner, Elmander (Taylor 73). Subs not used: Al Habsi, Hunt, Smolarek, Riga, Shittu.
Goals: Davies 30, Cahill 34, Taylor 86.
Booked: Nolan, Taylor, Andy O'Brien.
Att: 33,715
Ref: Mike Dean (Wirral).
BBC Sport Player Rater man of the match: Bolton's Gary Cahill on 7.09 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
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