Sammy Lee awaits his first win as Bolton boss after Fulham came from behind to win in torrential rain.
Healy (left) scored Fulham's opening goal
Tony Warner's blunder gifted Heidar Helguson a goal for Bolton before two quick goals goals by David Healy and Alexei Smertin put Fulham on top.
Healy equalised with a shot on the turn after a poorly cleared throw, before Smertin's long-range effort deflected in off Gerald Cid to put Fulham ahead.
El-Hadji Diouf and Nicolas Anelka went close but Fulham did enough to survive.
Fulham had the better of largely quiet opening period, notable only for its pouring rain, so it was a surprise when Bolton went ahead - and it was even more so considering how the goal came.
Warner looked to have gathered Nicky Hunt's long throw safely, but as he went to throw it clear, it slithered out of his grasp and rebounded off Zat Knight's back straight to the feet of Helguson.
The Icelander marked his first Bolton start with the simplest of finishes against his former club.
Healy marked his home debut with a goal when he stabbed home a poorly-cleared corner from close range, before another poor clearance gifted Fulham the lead.
Diouf conceded a free-kick near the right-hand flag and Simon Davis's weakly cleared cross fell to Smertin, whose optimistic long-range effort found the net courtesy of a huge deflection off Cid.
Fortunately the appalling weather improved after the break, making the game less of a lottery.
Shortly after the restart, Warner made amends for his earlier error with a superb full-stretch save from Anelka.
Diouf also flashed a shot across the goalmouth and just wide of Warner's right-hand post as Bolton took the initiative in the second half.
But despite dominating possession, they rarely turned that into serious goalscoring threats.
Fulham seemed to sense they had ridden the storm when they took off Healy and the creative Hameur Bouazza, sending on Kamara and Clinton Dempsey, and Kamara's physical presence gave them greater punch up front.
He wasted a great opportunity to settle the outcome when he failed to connect with a raking cross from close range.
But fortunately for Fulham they were not made to rue his error as they held on to win and continued their encouraging start to the season.
Fulham boss Lawrie Sanchez:
"We were just trying to work out the figures but I think David has scored something like 23 goals in 29 games under me as a manager so I had no doubts he would score goals.
"All I can do as a manager is give players the opportunity to perform at this level and give them the chance to prove they are good enough.
"Then it is all down to them so it is not about me being vindicated."
Bolton boss Sammy Lee:
"You have always got to be prepared to work hard in football. I knew that as a player, as a coach and now I know it as a manager.
"In football, you don't always get what you deserve.
"But the pleasing thing was the players' application and work ethic. They adapted to the conditions."
Fulham: Warner, Baird, Bocanegra, Knight, Konchesky, Davies, Smertin, Davis, Bouazza (Dempsey 80), Healy (Kamara 79), McBride.
Subs Not Used: Ricardo Batista, Volz, Diop.
Booked: Konchesky, Bocanegra.
Goals: Healy 23, Smertin 26.
Bolton: Jaaskelainen, Hunt, Cid, Meite, Samuel (Michalik 90), Nolan, Speed, McCann (Alonso 76), Anelka, Helguson (Braaten 72), Diouf.
Subs Not Used: Al Habsi, Sinclair.
Goals: Helguson 12.
Ref: Lee Probert (Gloucestershire).