West Brom striker Roman Bednar scored his first goal in open play this season to secure back-to-back Barclays Premier League wins for Tony Mowbray's side.
The former Hearts player, who had previously netted two penalties, broke the deadlock after 61 minutes to cap a second half dominated by the Baggies.
Albion were well worth their victory and can head into the international break full of confidence that they have the ability to finally establish themselves as a top-flight team.
Mowbray's faith in his strikers and midfielders to deliver sufficient goals after a stuttering start to the campaign is starting to be justified.
Bednar is looking more at home in the Premier League with every game, James Morrison is thriving on the flanks and in the middle of the pitch, Albion have the experience and know-how of skipper Jonathan Greening to fall back on.
And Mowbray looks to have picked up a real find in Dutch Under-21 international right-back Gianni Zuiverloon.
Fulham clearly missed the presence of the suspended Andy Johnson in attack and seldom posed a threat as the hosts kept a second successive clean sheet.
They have now lost all three league games away from Craven Cottage and could have few complaints about the result.
The first clear-cut chance fell to Bednar after seven minutes - but he failed to make the most of the opportunity.
Greening's reverse pass picked out the run of Bednar who got goal-side of Aaron Hughes but, after cutting back inside, he clipped his shot straight into the hands of Schwarzer.
Carson, in fine form in recent games, was called into meaningful action for the first time when he held onto a low curling drive from Clint Dempsey.
West Brom defender Jonas Olsson became the first player to be yellow-carded after 14 minutes for bringing down Dempsey just outside his own penalty area.
And Carson was relieved to see Jimmy Bullard's well-struck free-kick fly inches over the crossbar.
Former West Brom star Gera was receiving plenty of vocal support from the Baggies fans but he nearly silenced them on the half-hour mark when he came close to breaking the deadlock.
Dempsey set up the opportunity when he squared the ball back from the by-line into the path of the Hungarian and his precise side-footed effort flew only inches wide.
Borja Valero was booked by referee Phil Dowd for bringing down Gera with a late challenge.
Albion made a positive start to the second half and came close to going ahead within two minutes of the restart.
A deep cross from the left flank by Greening picked out Ryan Donk and the on-loan defender crashed a fierce header against the outside of a post.
Valero had a fierce drive blocked and then Bednar took a chip into the box from Robinson into his stride but volleyed wide.
The pressure was now relentless on the Fulham goal and a close-range header from Morrison was somehow cleared off the line by Danny Murphy.
But Fulham finally cracked after 61 minutes through Bednar's third goal of the campaign.
Greening's corner was turned back across goal by Donk and the former Hearts player was in the right place to stab the ball past Schwarzer.
It was no more than Albion deserved but they were nearly caught napping almost immediately by the Cottagers.
Bullard played a short free-kick to Murphy and his low 20-yard shot was deflected only inches wide,
Bednar had the chance to wrap up the points but Schwarzer did well to block his close-range effort from a Robert Koren center.
Schwarzer made a fine point-blank save to deny Bednar a second goal from a Koren cross.
Bednar also rattled the woodwork with a rasping drive from fully 40 yards which beat the dive of Schwarzer.