Nigeria striker Peter Odemwingie pounced on a defensive error to clip home a third-minute winner at Carrow Road for West Brom, which ended a run of three straight losses to climb into midtable.
"I think there will be a new atmosphere in the dressing room now," said Odemwingie, who was making his first start of the season after injury. "It was very important to win away, especially after three defeats."
Blackburn hung on for a draw at Craven Cottage after surrendering a lead given to the visitors by Spanish youngster Ruben Rochina, who smashed an unstoppable shot in off the underside of the bar from the edge of the area in the 32nd minute.
England striker Bobby Zamora equalized five minutes later for Fulham, leaving both teams stuck in the bottom three. Blackburn remained bottom, however.
"We've got spirit, we've got togetherness. We didn't sit back and just defend, we came with quite an attacking threat," said Blackburn manager Steve Kean, who has come under fire from supporters after the team's sluggish start to the season.
There was drama in second-half injury time when Blackburn striker Junior Hoilett broke onto a long clearance upfield and collided with Fulham goalkeeper Mark Schwarzer, who had rushed to meet the ball just outside the box.
Schwarzer was booked for the clumsy challenge and the game was stopped for several minutes while the Canadian Hoilett was treated and taken off the pitch on a stretcher.
Kean said the forward had lost consciousness and would need three or four stitches to a head wound.
While Blackburn could be destined for a long season at the foot of the table, West Brom have finally earned the win the team has deserved after unfortunate defeats to Manchester United, Chelsea and Stoke previously this season.
Roy Hodgson's side held on grimly after Odemwingie's early goal, which came when Ritchie de Laet failed to deal with Nicky Shorey's long ball forward, succeeding only in heading the ball into Odemwingie's path.
West Brom's top scorer last season showed great composure to guide his shot past goalkeeper Declan Rudd.
"I've been injured for a few weeks so I'm happy," Odemwingie said. "It's my first goal of the season and I am where I need to be, mentally."
The former Lille and Lokomotiv Moscow forward had a penalty saved in the 76th minute following Steve Morison's clumsy challenge on Steven Reid and was relieved that the miss didn't affect the result.
"In the last 10 minutes, I was praying they didn't get an equalizer," said Odemwingie.
Late pressure, including a couple of penalty appeals of their own, failed to yield an equalizer for Norwich, which is still looking for its first win back in the top division.
"I could not fault the lads for the way they played," said Norwich manager Paul Lambert. "We are still learning, but I am not despondent about the level of performance."
While Blackburn will be relieved to have ended its points drought, Fulham will wonder what might have been after failing to make the most of the team's second-half dominance, when midfielders Danny Murphy and Clint Dempsey went close to grabbing a winner.
"I'm really disappointed. I felt we dominated that match and we should have won it easily," Fulham defender Brede Hangeland said. "We lacked a little bit of skill and a little bit of luck."