That run stretched back to 1964, while it had also been more than five decades since they last scored more than once in a match against the Hoops, which they put right on this occasion to climb into eighth place.
Both sides fired in a number of shots in the opening stages of the match, but neither were able to show the quality required in front of goal to make a telling difference.
Just a few minutes later Andreas Bjelland caused panic with his looping header from a corner, which was hacked away off the line by a QPR defender, while up the other end Dan Bentley had to be alert to deny James Perch.
Hogan and Conor Washington both had chances to open the scoring for their respective sides as the first half wore on, but the opener did arrive prior to the break as Josh McEachran found Clarke, who was able to jink his way past one and then slot under Smithies.
Tjaronn Chery looked to start the QPR comeback by blasting into the arms of Bentley from 25 yards out, with the home side well on top in the opening stages of the second period.
Both teams again threatened to score without actually putting the ball in the net, though Sawyers did change that when arrowing into the top corner for his first Brentford goal.
There was to be one sour note for the Bees as Lewis Macleod was stretchered off in the final quarter of the match, but they did at least comfortably hold on for the remainder to earn three more points.