Striker bags the club's first ever triple in the Premier League to cap a dominant display which will ensure bragging rights over their neighbors for some time to come.
The home side completely overran its visiting rival with Johnson and captain Danny Murphy leaving to standing ovations after running the match, with Murphy also picking up a goal along with Bobby Zamora and Clint Dempsey.
QPR seemed to be starting brightly, with Shaun Wright-Phillips taking a snapshot that deflected into the arms of Mark Schwarzer in the opening minute. However, Fulham went straight up the other end and opened the scoring.
Moussa Dembele played a couple of neat one-twos with Johnson and Zamora before striking the ball low towards goal. Paddy Kenny got down well to make the save, but following in for the rebound was Johnson, who made easy work of the finish for his third goal in four days.
And it was almost two only minutes later as Dempsey got to the byline, with his cross deflecting first off Kenny then Fitz Hall, who made an acrobatic clearance to stop the ball crossing the line.
Steve Sidwell was booked shortly after for a cynical sliding tackle on mercurial midfielder Adel Taarabt, who seemed to be in some pain afterwards.
Fulham really were on the front foot, and almost added to the lead again in the 10th minute, with Dempsey arriving right on time to meet Johnson's low ball across the box, but his goal-bound effort was well blocked by Bradley Orr with Kenny already sent in the wrong direction by the American midfielder.
QPR was somehow surviving the siege the home side had mounted on its goal, this time Johnson went close with a volley from 25 yards that whistled past the post.
And a minute later, Johnson capitalized on a defensive mix-up between Hall and Kenny, getting in between the pair as the goalkeeper slid for the ball, upending the striker in the process to give away a penalty.
Murphy dispatched an unstoppable penalty into the top corner to give Fulham the two-goal margin they really did deserve for an outstanding opening 20 minutes.
Fulham added a third goal 10 minutes before the break with Johnson again in the right place at the right time. On this occasion, Murphy spread the ball wide to Riise, who played in Dempsey. The American turned before striking, but his shot was blocked and looked to be heading out for a corner until Zamora raced onto it and fired a ball across the six yard box for Johnson to stab home.
QPR came out sharper in the second half after making a double substitution, with Shaun Wright-Phillips offering the bulk of the attacking threat.
But if the game was in any doubt, Johnson put it to bed in the 60th minute by completing Fulham's first ever hat-trick in the Premier League.
The Cottagers were given a free kick roughly 40 yards from goal, and captain Murphy took it quickly to devastating effect, playing Johnson in around the side of a QPR defense firmly on the back foot for the striker to roll the ball past Kenny.
And it was not anywhere near over, as Zamora looked to find the net with two efforts in the space of a couple of minutes, the first testing Kenny and the second flashing just wide.
Moments later, Fulham added a fifth, as Johnson went wide on the left before striking a low cross into the center. The ball was slightly behind Zamora, who deftly flicked it into the path of the on-rushing Dempsey to fire home.
Zamora got the goal he deserved with 15 minutes to go as he pulled his shot into the far corner from the edge of the penalty area after Kenny had been unsighted, and it capped a wonderful afternoon for Fulham and their fans, while QPR boss Neil Warnock will have plenty of questions to ask of his team in the coming week.