El Hadji Diouf tested Joe Hart with a rasping shot and, soon after, he sent in a wicked low cross that just eluded Matthew Taylor and Danny Guthrie and was cleared by Vedran Corluka.
From the ensuing corner, which was taken by Senegal star Diouf, Steinsson was first to the ball and sent his header crashing against the post.
But City survived the early storm and threatened themselves when Petrov's corner was cleared as far as Ireland, who fired in a rasping shot that was headed off the line by Gardner.
Bolton continued to push forward after the break but they were struggling to turn their possession into chances.
And it was City who had the next golden opportunity when Benjani ran clear but he dithered on the ball and, although Elano eventually got a shot away, the opening was wasted.
Only in the final half-hour did the game truly open up and several chances went begging at both ends.
Steinsson's header was blocked by the impressive Richard Dunne before a last-ditch tackle by Elano denied Davies.
Another Steinsson effort was deflected clear and Hart produced a fine save to keep out Diouf's shot from a tight angle.
City were threatening too and Elano's drilled 30-yard shot was pushed away by Ali Ab Habsi before O'Brien's heroic block kept out Caicedo's goalbound effort.
Bolton could still have had the final word when Davies rose to head towards the bottom corner but Petrov was in the right place to clear and ensure his side earned a point.
Bolton's Ricardo Gardner will have an X-ray on a rib injury after being carried off on a stretcher late in the first half. The Jamaica midfielder landed awkwardly under a challenge from Darius Vassell.
Bolton boss Gary Megson: "We have drawn a game we maybe should have won but not through a lack of effort.
"We gave their goalkeeper a lot to do and we certainly could not have tried any harder.
"We had a lot of efforts on goal so there is a lot to be positive about but at this stage of the season it is all about getting the three points."
Manchester City manager Sven-Goran Eriksson: "Bolton are fighting for their lives. You have to cope with the way they play and defensively we did okay.
"Richard Dunne was extremely important to us in dealing with the amount of long balls and crosses they put in.
"We dealt with them well but we hit too many long balls ourselves and in the future we have to play more football."
Bolton: Al Habsi, Steinsson, Cahill, Andrew O'Brien, Gardner (Joey O'Brien 46), Diouf, Nolan, Campo (McCann 63), Guthrie, Taylor (Giannakopoulos 83), Davies. Subs Not Used: Walker, Rasiak.
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