Victory temporarily lifted Wanderers into the Champions League place that everyone at the ambitious club craves.
Allardyce says he would swap that achievement for an FA Cup final win and, with Fulham brushed aside, the Trotters chief can concentrate on the second part of his potential weekly treble with a fourth round cup replay success over Arsenal.
The Gunners will be a tougher prospect than fragile Fulham, whose away form continues to give manager Chris Coleman cause for concern.
Bolton rarely had to break sweat to achieve the three points, but they almost slipped up at the death
Only Jussi Jaaskelainen prevented Fulham gaining an unlikely draw with a smart save from Tomasz Radzinski.
Had it gone in, Allardyce would have been livid but as it was he still finished with a smile on his face.
Wanderers gained their win without three key players - Ivan Campo and Abdoulaye Faye and Kevin Davies.
Gary Speed's first-half penalty set Wanderers on their way and skipper Kevin Nolan's 51st minute effort effectively killed off the contest.
However, Zat Knight took advantage of some slack marking to give the Cottagers a lifeline they barely deserved.
In the end it proved nothing more than a consolation, but Bolton can ill afford the same complacency against Arsene Wenger's men.
The game needed a spark to liven it up after a sterile 20 minutes and it arrived with the award of a penalty against Fulham.
Skipper Michael Brown was adjudged to have pushed Nicolas Anelka in the back and Speed tucked away his fourth goal of the campaign.
Despite Fulham protests, the Frenchman was poised to shoot after Knight failed to cut out a cross from the byline.
The visitors suffered further trouble soon after. Heidar Helguson was injured and cautioned for a needless late challenge on Jaaskelainen with the Finn already in possession of the ball.
Bolton could have been out of sight by half-time. Andranik Teimourian, back from midweek international duty with Iran, wriggled his way to the byline and picked out Diouf but the unmarked Senegal star ballooned over the bar.
Simon Davies then became the third Fulham player yellow carded in the opening 45 minutes for a foul on Ricardo Gardner.
Stelios and Anelka carved out another chance for the home side but Andranik's final shot from 18 yards was tipped to safety by Jan Lastuvka.
The keeper had no chance with Bolton's second four minutes after the restart. Nicky Hunt's looping cross was headed against an upright by Stelios but the ball broke invitingly for Nolan to join Diouf, Campo and Davies on five for the season.
That should have been that but Knight gave the visitors hope and only Jaaskelainen's wonder save preserved Bolton's advantage.