The Wanderers captain - making his 500th career appearance - looked to have won it for the hosts when he planted a firm header past Mark Schwarzer.
But referee Mark Clattenburg mysteriously spotted a foul as Chung-Yong Lee's free-kick came over and chalked off the late 'winner'.
It was one of the few moments of interest in a woeful 90 minutes of football which leaves Owen Coyle's men one place above the relegation zone.
Injury-hit Fulham, without Bobby Zamora, Andy Johnson, Clint Dempsey, Zoltan Gera and John Paintsil, had ended a run of six Premier League games without a win by beating Portsmouth in midweek, but they looked to have come to the Reebok Stadium for a point from the start.
The game's first opportunity came after just three minutes when Paul Robinson picked out Tamir Cohen but the midfielder's header lacked the power to trouble Mark Schwarzer in the Cottagers goal.
Without his first-choice strike duo, Roy Hodgson handed a first start to David Elm and the Swede went close when he turned over Jonathan Greening's corner on 11 minutes.
The best chance of the first half fell to Mark Davies when his namesake Kevin headed back across the six-yard box but the midfielder's attempt cannoned up off Schwarzer's leg and onto the underside of the crossbar.
The second half proved even more disappointing than the first as both sides struggled to carve out clear-cut opportunities.
The closest Fulham came was when Nicky Shorey's deflected free-kick flew just over, much to the relief of a wrong-footed Jussi Jaaskelainen.
Substitute Johan Elmander wasted a superb opportunity to win it with a minute left when Kevin Davies sent him clear but the Swede failed to hit the target.
Kevin Davies then thought he had saved the day for Bolton but Clattenburg's whistle came to Fulham's rescue.