There were a few half-chances and Fulham went close with efforts from Andy Cole and Papa Boupa Diop but in the end a strong Wanderers defence was able to hold on for their first win over the London side in ten attempts.
Wanderers boss Sam Allardyce has insisted that success in the FA Cup is the best way to ensure UEFA Cup qualification, yet regardless of that he still fielded a side showing five changes.
Regular first-teamers El-Hadji Diouf and Ivan Campo were not included in the squad, while Kevin Nolan, Ricardo Gardner and Anthony Barness, who all figured in last week's Premiership draw with Middlesbrough, were among the substitutes.
In their place came right-back Nicky Hunt, who had been sidelined since being injured in the fourth round tie at Oldham, top scorer Henrik Pedersen, midfield men Fernando Hierro, Khalilou Fadiga and French left-back Vincent Candela, who was making his debut after signing a loan deal until the end of the season following his release by AS Roma.
Fulham boss Chris Coleman, however, was happy to make only one change from the side that won their hard-fought fourth round replay against Derby last week.
Alain Gorma, who came on as a substitute in that game, was preferred to Zesh Rehman, while former Wanderer Claus Jensen, also a sub last week, kept his place on the bench.
The two sides went into the match with impressive recent records. Wanderers were unbeaten in their last nine games, while Fulham had only one defeat in their last ten games.
And it was Wanderers who got the all-important good start. They had looked good in the opening minutes with some neat passing movements, and that was put to good use in the 11th minute with a goal fashioned out of good movement and astute approach play.
Davies ducked under Hunt's cross, then ran round the Fulham defence to receive Pedersen's throughball and push the ball past Edwin Van der Sar for his eighth goal of the season.
The goal, however, failed to inspire Wanderers into producing more attacking play, and it was the London side that picked up on the initiative to move forward.
Cole hit a snap-shot that was only just too high and a long-range effort from Diop also flew over the bar. And when Cole picked up a poor clearance from Jussi Jaaskelainen, the Wanderers keeper was relieved to see the striker's shot fly wide of a post.
The first five minutes of the second period contained almost as much attacking play as the whole of the first half and the crowd was woken out of its slumber by two teasing Hierro crosses into the six-yard box that brought good saves from Van der Sar after a certain amount of panic by his defenders.
That also spread to Wanderers defenders as well but Cole failed to get his shot on target after getting the wrong side of Tal Ben-Haim, while Candela was
Left stranded by Liam Rosenior's trickery on the edge of the area.
Yet it all failed to produce any real threat to either goal, Van der Sar cutting out one effort as Bruno N'Gotty rushed in at the far post, then Jaaskelainen foiling Cole before pushing a powerful shot from Tomasz Radzinski over the bar.
If anything, it did serve to add some spark to the play and for almost the first time in the game, the two sides started to show a little passion in their play.
Diop added to Fulham's growing list of off-target shots when he fired over the bar, while at the other end Jay-Jay Okocha should have done better on the edge of the six-yard box when he failed to connect with a header from Hunt's cross.
Wanderers should have added to their lead in the 70th minute when Okocha rounded Van der Sar and fashioned a chance for Pedersen to fire at an almost empty net, only for his weakly hit shot to be beaten away by a retreating defender.
That was Pedersen's final kick as he made way for Nolan, while Wanderers also brought on Gardner for Fadiga, and Fulham introduced Jensen for Sylvain Legwinski, Collins John for Luis Boa Morte and Brian McBride for Cole.
Fulham seemed to benefit from the changes rather than the home side, forcing two corners in quick succession, but on each occasion, Jaaskelainen was equal to the test.
Okocha was substituted six minutes from the end by Anthony Barness but not before he forced Van der Sar into a good, low save although that was something of a rare occurrence by Wanderers. They yielded space to a Fulham side that quickly responded with Diop planting a header at goal that Gardner hacked off the line.
Barness then had to block another on the line from Jensen as Fulham staged a grandstand finish before a grateful Jaaskelainen was able to pounce on the ball.
MAN OF THE MATCH: Bruno N'Gotty (Bolton): A towering performance by the French defender, who manager Sam Allardyce hails as the best signing he has made while at Bolton.