Josko Gvardiol bagged the opener and the defender struck again after Phil Foden's goal before Julian Alvarez's stoppage-time penalty sealed a commanding performance at Craven Cottage.
Guardiola's side are two points clear of second placed Arsenal, who travel to Manchester United for their penultimate game on Sunday.
If Arsenal fail to beat United, then City can wrap up an unprecedented fourth successive English title with a victory at Tottenham on Tuesday.
Even if Arsenal beat Erik ten Hag's men, City would still clinch a remarkable sixth title in seven seasons if they defeat Tottenham next week and see off West Ham at the Eithad Stadium on May 19.
"Since they (Arsenal) lost against Aston Villa the destiny is in our hands," Guardiola said.
"In the last game of the season against West Ham the destiny is in our hands and that is what we want. It will be difficult but we are ready for the challenge."
City overcame an eight-point deficit in the title race last season to catch Arsenal and take the trophy.
They have also came out on top in tense title races with Liverpool during Guardiola's dynastic reign.
And, with City now unbeaten in 21 league games, the Spaniard saluted his players' ability to thrive under duress.
"My players like to play with pressure, they are used to it. The players enjoy this feeling," Guardiola said.
"This season is the same, don't think about anything other than the next game. Focus on winning the next game and then we will see what happens. We go to London and try to win."
