The visitors started to see more of the ball as the first half progressed though, and came close to opening the scoring inside the final 10 minutes of the first spell when Jay Emmanuel-Thomas created openings for Matt Phillips and Tjaronn Chery, but neither could find the back of the net.
QPR continued to look lively in the final minutes of the half, but Massimo Luongo was twice denied by the woodwork, heading against the crossbar from a Phillips cross before striking the post moments later.
Brentford tried to get back on the front foot at the start of the second half as Djuricin forced a save from Green, before Swift blasted the ball high on the rebound.
The home side opened the scoring just over 10 minutes after the restart as Alan Judge delivered a low cross from the left to set up Djuricin for a tap-in to put Brentford ahead.
Green had to remain alert to stop the Bees doubling their lead soon after as Judge tried to pick out the top corner with a curling free kick from the edge of the box, but the keeper did just enough to keep it out.
Seeking an equaliser, the visitors brought on Charlie Austin inside the final half-hour for the striker's first appearance after more than a month out injured, but it was the home side who continued to press. However, Bidwell could not keep his header down after McCormack picked him out with a cross.
Brentford kept the pressure on with Judge crossing in from out wide, but none of his teammates was there to make the most of it, while Swift looked for Konstantin Kerschbaumer late on.
Austin was kept quiet for the majority of his spell, but he did get into a dangerous position in the final 10 minutes when Phillips delivered a cross from the right, although Brentford cleared before the forward could reach it.
The visitors were still trying to find the elusive equaliser as the match headed into stoppage time, forcing a corner which allowed Junior Hoilett to get a shot away, but the finish was blocked, ensuring that the Bees claimed the three points.
The result, which is the Bees' first win over the Hoops since 1965, lifts Brentford up to 10th in the table, leapfrogging tonight's opponents, who drop to 11th.