The Croatia international showed all the poise of a seasoned striker to put Man City in front inside the opening 15 minutes.
After taking a narrow lead into the half-time break, Man City doubled their advantage thanks to Phil Foden's 59th-minute strike.
Gvardiol then added his second and the visitors' third, before Julian Alvarez came off the bench to dispatch a stoppage-time penalty after Issa Diop committed a clumsy foul to receive his second yellow card.
The comfortable victory eliminates Liverpool from the title race and leaves Man City two points clear of second-placed Arsenal with just two games left to play.
Gvardiol gives Man City half-time lead
Man City began the contest in second place, knowing a win would move them into pole position and shift the pressure onto title rivals Arsenal.
The reigning Premier League champions required just 13 minutes to break the deadlock at sun-drenched Craven Cottage.
Following some patient build-up play, Gvardiol exchanged a neat one-two with Kevin De Bruyne, before cutting across Issa Diop and sending a low strike past Bernd Leno.
After moving in front, Man City quickly began their search for a second, with Bernardo Silva and Foden forcing Leno to make a couple of routine stops.
Despite controlling the first period, the Citizens had to settle for a slender half-time lead after Manuel Akanji spurned the chance to double his side's advantage in the 44th minute.
The Switzerland international could only lift the ball harmlessly over the bar from De Bruyne's dangerous inswinging delivery.
After seeing his side fail to muster a single shot in the first half, Marco Silva decided to make a double change at the break, introducing Adama Traore and Tom Cairney.
Champions move through the gears
The changes could not prevent Man City from carving out the first chance of the second period, with Silva firing a near-post shot at Leno after being teed up by De Bruyne.
Fulham then experienced a brief moment of promise as Traore sent a low cross in for Rodrigo Muniz to flick goalwards, but the lack of power allowed Ederson to make a comfortable stop.
However, Fulham's hopes of claiming a positive result were dealt a major blow when Foden found the net just before the hour mark.
The England international pounced on a loose ball to sweep a right-foot strike into the bottom corner to register his 17th league goal of the season.
As the contest entered the final 20 minutes, the Citizens produced another moment of quality for Gvardiol to add his second of the game.
The visitors worked a corner to the edge of the box for Silva to send a deep cross towards Gvardiol, who stuck out a leg to squeeze the ball past Leno to net his fifth goal in seven appearances.
Alvarez rounds off commanding display
With the three points wrapped up, the Citizens were given the chance to take their tally to four when Diop brought down Alvarez with a tired-looking challenge.
The defender was given his marching orders for two bookable offences, before Gvardiol declined the opportunity to take the penalty and a chance at a potential hat-trick.
Alvarez was more than happy to oblige with Gvardiol's wishes, stepping up to fire his spot-kick into the bottom corner.
Man City have now won each of their last seven league games and are on the verge of claiming a fourth consecutive title.
The Citizens will have one eye on Sunday's clash between Arsenal and Manchester United, before they turn their focus to Tuesday's meeting with Tottenham Hotspur Hotspur.
As for Fulham, they have now failed to win four consecutive matches, leaving them in 13th place with 44 points to their name.