Jol admitted in the build-up that a defeat to their London rivals would leave him fearing for his job, having overseen their worst ever start to a Premier League season.
Modibo Maiga had the first half's best chance as he headed an effort against the post, but goalmouth action was infrequent for the rest of the period.
The hosts did have the lead less than 60 seconds after the break, however, as Fernando Amorebieta deflected a Mohamed Diame shot past Maarten Stekelenburg.
Carlton Cole and Joe Cole scored in the closing stages to seal an emphatic scoreline for West Ham's 12 Premier League matches, while Jol’s team suffered a fifth successive loss.
Sam Allardyce made four changes from last week's defeat to Chelsea, Matthew Jarvis and Diame recalled.
Swansea City were Fulham's conquerors last time out and boss Jol named three alterations to that team as he dropped Bryan Ruiz and Derek Boateng, while captain Dimitar Berbatov missed out through illness.
The hosts dominated the early proceedings and nearly took the lead 10 minutes in as Modibo Maiga directed Mark Noble's right-wing free-kick goalwards, but it struck the post.
Stekelenburg was forced into his first save of the match seven minutes later as Stewart Downing cut in from the right and fired a long-range effort towards the bottom corner, but the Dutch goalkeeper palmed the strike away.
With just a few minutes of the first half remaining Kevin Nolan looked set to score as he met Downing's chipped cross with an acrobatic scissor-kick, but the attempt bounced up and into Stekelenburg's hands.
Following their struggles in front of goal in the first period, it took West Ham less than a minute to open the scoring after half-time as Diame stole possession from Scott Parker and then saw his 20-yard effort deflected into the net off Amorebieta.
Just after the hour-mark the hosts had two headed opportunities in quick succession as James Tomkins directed a corner agonisingly wise and Jarvis knocked the ball straight at Stekelenburg, before Downing’s cross struck the crossbar.
With just eight minutes remaining, Allardyce's men made sure of the win as Carlton Cole latched on to Downing's low cross and poked the ball home for his first goal since December 2012.
There was still enough time for Joe Cole to find the net in the 90th minute following an excellent Ravel Morrison run to heap the misery on Fulham and Jol.
