Fulham gained their first point under new manager Roy Hodgson in a match that lacked any flashes of quality at the Reebok Stadium.
Both sides battled hard for possession but quality was lacking
The Cottagers, without a Premier League away win since September 2006, had the best of the first half with new signing Leon Andreasen shooting just over.
But Bolton should have scored after the break when Lubomir Michalik cushioned the ball wide with the goal gaping.
Fulham are now four points from safety while Bolton slip to 16th in the table.
The visitors, still without a win under Hodgson, had the better of the opening exchanges.
In the 10th minute, Danny Murphy found space in a congested midfield to slip a pass through for Clint Dempsey but Fulham's lone striker hammered the ball high and wide of Jussi Jaaskelainen's goal.
New Danish international signing Andreasen was quick to hit the ground running on his debut, shooting just over from 20 yards and showing resolute defending whenever Bolton applied pressure.
Their best chance came when Danny Guthrie broke into the box but the 20-year-old midfielder, on loan from Liverpool, dragged his low shot wide.
Jimmy Bullard, making his first Fulham start since major knee surgery, also went close when he whipped a 15-yard skimmer wide of the post.
Fulham continued to boss possession, with Dempsey a lively runner, but the United States international lacked support in attack.
But Bolton looked rejuvenated after the half-time break and nearly took the lead in the 58th minute.
New-boy Gretar Steinsson broke down the right wing and his cross just eluded fellow home debutant Matt Taylor at the back post after being flicked on by Kevin Nolan's backheel.
With Taylor peeling in from the left-wing, Bolton's threat continued to increase and Fulham were forced to concede a number of free-kicks around the box.
Guthrie floated the best of these over Fulham's defensive wall and into Antti Niemi's arms before being substituted for Iranian midfielder Andranik Teymourian on 73 minutes.
Moments later, Slovakian defender Michalik missed the best chance of the match when he cushioning the ball just wide with the goal gaping after a stranded Niemi had failed to punch clear.
After a raft of substitutions, both teams seemed content to cut their losses and play out for a point.
Bolton manager Gary Megson:
"The frustration was clear for all to hear from the fans at the end but you could see the Fulham players were delighted to come away with a point.
"We needed to score to settle down a bit but there's going to be a lot of games up and down the country like that at the moment.
"We are down in the bottom six or seven but that might prove to be a decent point at the end of the season, though our quality wasn't there today.
"We have to take a positive from tonight and that's a clean sheet."
Fulham boss Roy Hodgson:
"The point gives me a lot encouragement in terms of the way the team played.
"In the second half our players were tired and we didn't get hold of the ball so much, but we defended very well throughout.
"My group of players are good professionals who want to improve, work hard at their game, and roll up their sleeves and show the neccessary fighting spirit to get us through.
"Tonight was a big step forward, we've got 14 games left to go, and we certainly aren't throwing in the towel."
Bolton: Jaaskelainen, Steinsson, Andrew O'Brien, Michalik, Gardner, Joey O'Brien (Cohen 46), Guthrie (Teymourian 68), McCann, Nolan, Taylor (Helguson 83), Davies.
Subs Not Used: Al Habsi, Samuel.
Fulham: Niemi, Baird, Hughes, Hangeland, Konchesky, Volz (Christanval 74), Andreasen (Bocanegra 83), Murphy, Bullard (Bouazza 87), Davies, Dempsey.
Subs Not Used: Warner, Healy.
Ref: Mark Clattenburg (Tyne & Wear).
BBC Sport Player Rater man of the match: Fulham's Clint Dempsey 6.84 (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.