Wanderers were left frustrated as a resilient Fulham defence and a dubious disallowed goal denied them a deserved three points.
Kevin Davies looked to have won the game for Bolton in the 90th minute when he towered inside the penalty area to head home Chung-Yong Lee's free-kick.
But referee Mark Clattenburg chalked off the goal, deeming that skipper pushed Brede Hangeland in the back.
The late strike would have been just rewards for Bolton for a dominant performance against Fulham, who offered precious little in attack.
Bolton asked all the questions and could have easily won by a comfortable margin had it not been for a bit more fortune in front of goal and two wonderful saves from goalkeeper Mark Schwarzer.
Wanderers were already without the services of the previously ever-present Gary Cahill through injury, but Owen Coyle was dealt a further blow when Gretar Steinsson was deemed unfit to play after being named in the original starting line-up. Therefore Andy O'Brien and Paul Robinson came into the team, with Sam Ricketts moving across to right-back.
There was a leisurely pace to the game as the afternoon's events started in bright winter sunshine. The first ten minutes passed without any noteworthy action up until a half-chance for new signing David Elm, whose stretched finish at the far post drifted just wide of the target.
Kevin Davies had a penalty shout rejected when he seemed to be toppled by a challenge from Brede Hangeland as Bolton started to play themselves into the contest.
Despite passing the ball around with confidence and dominating possession, Fulham contained Wanderers in the final third, with Tamir Cohen's volley from the edge of the box being the only real shot on goal in the first quarter.
Schwarzer saved Ricketts' header following an inviting Taylor free-kick while South African Kagisho Dikgacoi blazed fractionally wide for Fulham with a 30 yard effort before the half ended with a flurry of activity.
Firstly Muamba drove forward from midfield, struck an effort that deflected up into the path of Cohen but just as the Israeli international tried to bring the bouncing ball under control, he was crowded out inside the six-yard box.
And then, just two minutes later, Schwarzer produced a fantastic save to deny Mark Davies. The diminutive midfielder hit a fierce goalbound effort from 12 yards that struck the Australian stopper and flew up on to the crossbar.
With no changes made by either manager at the break, Bolton came out of the blocks the quicker as Cohen shot wide with a 20 yard volley and a Matt Taylor free-kick hit a wall.
With 57 minutes played, Johan Elmander was thrust into the action and it didn't take long for the Sweden striker to make an impact. Just seconds after coming onto the field he went up for an aerial challenge with Hangeland, and after a clash of heads, play was held up for a short while.
Owen Coyle had already had to deal with two defensive casualties prior to kick-off and it became three when Andy O'Brien was forced to leave the field. Chris Basham, who hadn't even made the team sheet at 2pm, was introduced with Ricketts moving into the heart of the rearguard.
In the face of the defensive crisis, Wanderers fans rallied behind the team in their quest for the important breakthrough goal and the substitution of the Vladimir Weiss and further impetus.
Again, the Whites were only a Schwarzer save away from attaining that when Chung-Yong ran clear after playing a neat one-two with Cohen on the edge of the box. But just as the South Korean appeared to round the goalkeeper, an outstretched arm palmed the ball to safety.
For all their dominance, Bolton still needed to be wary of Fulham's attacking threat, none more so when Nicky Shorey's free-kick flicked up off Kevin Davies and ricocheted just inches over Jaaskelainen's crossbar.
Owen Coyle knew that it wasn't going to be his team's day when Johan Elmander shot just wide having been released by Davies before the captain saw his seemingly good goal disallowed with time almost up.
Bolton: Jaaskelainen, Ricketts, O'Brien (Basham 63), Knight, Robinson, Taylor (Weiss 70), Cohen, Muamba, Chung-Yong, Mark Davies (Elmander 57), Kevin Davies (Subs: Samuel, Gardner, Al Habsi, Wilshere)
Fulham: Schwarzer, Hangeland, Baird, Shorey, Murphy, Nevland (Smalling 75), Duff, Hughes, Greening, Dikgacoi (Etuhu 55), Elm (Okaka 75) (Subs: Zuberbuhler, Kelly, Riise, Stoor)