Raul Jimenez opened the scoring in the fifth minute after taking taking the ball down in the penalty area from an Adama Traore cross, before drilling an unstoppable effort into the bottom-right corner past Nick Pope.
Emile Smith Rowe poked a second goal past the Newcastle keeper after he combined well on the left flank with former Arsenal teammate Alex Iwobi, who played a pass into the box which Smith Rowe latched onto.
Eddie Howe's team got into the game after Harvey Barnes picked up from where he left off against Tottenham and scored just after half time at Craven Cottage.
The Toon dominated the ball in the second 45 minutes but despite good attempts from the likes of Anthony Gordon and Fabian Schar, the home side would go on to score a third in stoppage time thanks to Reiss Nelson.
Newcastle stay on 10 points while Fulham end the day with eight points and are now unbeaten in their last four Premier League games.
Silva will be delighted with his team's start to the 2024-25 Premier League campaign and will be thrilled that his side have managed to claim all three points against Newcastle, who they had lost to in all six of the clubs' prior meetings.
Highlights
5th min: Fulham 1-0 Newcastle United (Raul Jimenez)
Raul Jimenez drops deeper into midfield and plays the ball out wide to Adama Traore on the right flank, and crosses towards the Jimenez, who hosts strikes brilliantly into the bottom-right corner.
Nick Pope had no chance!
12th min: Fulham 2-0 Newcastle (Emile Smith Rowe)
Emile Smith Rowe combines down the left flank with Alex Iwobi, who plays a pass back to Smith Rowe inside the box and the summer signing pokes the ball at Pope, who fails to stop the shot from trickling in after his attempted save.
A second goal for Smith Rowe at Fulham!
46th min: Fulham 2-1 Newcastle (Harvey Barnes)
Jacob Murphy bursts forward from inside his own half after winning the ball back, and plays a pass to Harvey Barnes on the left of the box, and the winger finished into the bottom right corner past Bernd Leno.
Harvey Barnes pulls one back for the Toon!
92nd min: Fulham 3-1 Newcastle (Reiss Nelson)
Bruno Guimaraes attempts to play a pass from the left of the pitch to right from inside his own penalty area, but he fires the ball straight to an unmarked Reiss Nelson in the box, and he fires home from just yards out.
What was Guimaraes thinking?
Man of the match - Emile Smith Rowe
Emile Smith Rowe had 89% pass accuracy, played four passes into the final third and also found the back of the net in the first half.
The Cottagers attacker found it difficult to break through the ranks at Arsenal, but he has shown great signs of promise under Silva in the early stages of his Fulham career.
BEST STAT
MATCH STATS
Possession: Fulham 39%-61% Newcastle United
Shots: Fulham 22-15 Newcastle United
Shots on target: Fulham 11-4 Newcastle United
Corners: Fulham 6-0 Newcastle United
Fouls: Fulham 16-8 Newcastle United
What next?
Fulham will play Nottingham Forest in the Premier League next Saturday at the City Ground before an away trip to the Etihad Stadium on October 5.
As for the Toon, they face AFC Wimbledon in the third round of the EFL Cup on Tuesday The Cherry Red Records Stadium, and will face Manchester City on September 28.