Kevin Nolan's deft volley in stoppage time rescued a point for Bolton.
McCartney scores his first goal for West Ham
George McCartney's superbly executed first-half volley put West Ham ahead and soon after he protected their lead by heading clear El-Hadji Diouf's shot.
Bolton's Danny Guthrie then had a low shot that hit the upright, while Kevin Davies went agonisingly close when his header skimmed off the bar.
Jussi Jaaskelainen saved well from Carlton Cole before Nolan showed a striker's instincts with his goal.
Bolton remain second from bottom in the table and have still only managed one win this season.
Bolton were without the injured Nicolas Anelka and considering the number of chances they had, the visitors might have won this game had he been available.
Given McCartney has scored just one goal in his professional career - for Northern Ireland - he was an unlikely candidate to be the game's first goalscorer.
Bolton had spurned several opportunities to clear the ball following a West Ham corner and McCartney - with both feet off the ground - expertly volleyed the ball past Jaaskelainen to punish Megson's side.
The goal was reward for West Ham's bright beginning to the game with Matthew Etherington always purposeful, delivering a series of dangerous crosses from the left wing.
Etherington delivered the pass of the game in the second half when he flighted the ball to the feet of Cole.
The former Chelsea striker's shot was partially saved by Jaaskelainen and Cole was unable to prod in the rebound.
Going behind to McCartney's goal seemed to awaken Bolton from their rather ponderous start and Diouf's deflected shot, which looped over Robert Green, was headed clear by the Northern Ireland international.
Green was soon beaten again as Guthrie's low shot ricocheted off the post.
In the opening few minutes Guthrie had incurred the wrath of Lee Bowyer after tackling the West Ham midfielder with both feet raised off the ground, with his studs showing.
As in the first half Bolton took their time to get going in the second period and it took them 15 minutes to mount a serious attack when Gary Speed's shot was tipped over by Green.
Just before conceding the goal West Ham had a lucky escape when Jonathan Spector hacked the ball off the line.
Nolan's goal arrived in the third minute of injury when the Bolton midfielder pounced on Lubomir Michalik's header and flicked the ball past Green.
West Ham boss Alan Curbishley
"It feels like a defeat. We played the last 10 minutes like we were losing the game when it needed a bit of professionalism.
"We had opportunities to run the clock down and kill a bit of time.
"We're so disappointed, that's a big two points we have dropped. We scored early and took our foot off the pedal."
Bolton boss Gary Megson:
"I think overall it was a fair result, something we deserved. Kevin had a terrific opportunity and we had two cleared off the line.
"To come down here and get a point in the manner we did is a big fillip. It's a difficult place to come.
"We will get better at the technical aspects but in terms of the human things, they were there in spades."
West Ham: Green, Neill, Gabbidon, Upson, McCartney, Boa Morte, Solano, Mullins (Spector 50), Bowyer (Pantsil 85), Etherington, Cole (Camara 72).
Subs Not Used: Wright, Reid.
Booked: Bowyer, Pantsil.
Goals: McCartney 20.
Bolton: Jaaskelainen, Hunt (McCann 81), Andrew O'Brien, Meite (Michalik 46), Gardner, Diouf, Guthrie, Nolan, Campo, Speed (Samuel 78), Davies.
Subs Not Used: Al Habsi, Giannakopoulos.
Goals: Nolan 90.
Ref: Peter Walton (Northamptonshire).