Both teams had chances to open the scoring before Muniz found the net in the closing stages of the first period to give the hosts a slender half-time lead.
Buoyed by their opener, Fulham moved through the gears after the break to add a second and third through Sasa Lukic and Muniz respectively.
Fulham then saw a potential fourth goal ruled out, but it mattered very little, as they stood firm to become their first team to stop Tottenham from scoring in a Premier League game this season.
While 12th-placed Fulham can celebrate their first home league victory over Spurs since November 2008, the visitors are left to reflect upon a disappointing performance which leaves them in fifth spot and two points adrift of the top four.
Fulham began the contest on the front foot, with Andreas Pereira forcing Cristian Romero to make a crucial block shortly before Guglielmo Vicario was required to keep Lukic at bay.
After soaking up the early Fulham pressure, Tottenham started to grow into the contest and offer their own threat in the final third.
Wales international Brennan Johnson would have been disappointed to guide a tame effort straight at Bernd Leno after being teed up by James Maddison's well-weighted pass.
Maddison then attempted to catch Leno off-guard with a near-post strike, but the former Leicester City man could only send his shot wide of the German's goal.
Just as it seemed as though momentum was swinging in Tottenham's favour, Marco Silva's side wrestled back control thanks to Muniz's 42nd-minute effort.
The Brazilian collected Antonee Robinson's inch-perfect cross, before keeping his composure to slot into the bottom corner.
Ange Postecoglou would have been desperate to see a positive response from his team after the break, but the Spurs boss could only watch on as Fulham doubled their advantage within four minutes of the restart.
Lukic stuck out his left knee to divert Timothy Castagne's cross beyond the helpless Vicario to register his first goal for the West London club.
With Spurs on the ropes, a confident Fulham side went on the hunt for a third, with Castagne forcing Vicario into a near-post stop.
However, the Tottenham goalkeeper could do nothing to prevent Muniz from grabbing his second of the game in the 61st minute.
The 22-year-old pounced on a rebound after Calvin Bassey had thumped the post to tap in his seventh goal in as many matches.
With momentum firmly in their favour, Fulham thought they had added a fourth when Joao Palhinha's drilled strike flicked off Raul Jimenez and into the net, but the goal was swiftly chalked off for an offside infringement against the Mexican.
Timo Werner and Richarlison both spurned chances to get Tottenham on the board in the final quarter, but those misses ultimately summed up a forgettable outing at Craven Cottage.
Vicario at least managed to stop Fulham from netting a fourth in stoppage time, making a strong save to keep Harry Wilson's powerful effort out.
With the Premier League set to stop for the international break, Fulham will return to action against Sheffield United at the end of the month, while Spurs will look to get back on track in a home meeting with Luton Town on March 30.