Dozzell’s powerful strike from outside the area two minutes before half-time put Gareth Ainsworth’s side in command at the Riverside.
And the 24-year-old midfielder, who moved to Loftus Road two years ago from Ipswich, was among the celebrations 19 minutes from time when Jack Colback hammered in the QPR’s second.
It was a much-needed second victory of the season for QPR but one that has left Michael Carrick’s Middlesbrough without a win in five league games.
Neither side posed a threat to either of the goalkeepers in the opening exchanges, despite QPR finding the space down the flanks.
Ilias Chair, who remained at QPR despite reported transfer window interest from Leicester, was involved down the left a couple of times in the opening few minutes.
The Morocco international was able to get to the byline and pick out a team-mate in the area on both occasions without troubling former Rs keeper Seny Dieng’s net.
When QPR did push forward through Chair, Kenneth Paal or Paul Smyth down the opposite flank, Middlesbrough were alert to prevent shots hitting the target.
And it was a similar story in the opposite direction, where Isaiah Jones, Sammy Silvera and Morgan Rogers looked the most likely to create something early on for the hosts.
But the only real chance of note in the first 40 minutes was when Jones controlled a Silvera pass before his shot was stopped by the foot of Asmir Begovic.
That arrived in the 25th minute and Middlesbrough striker Emmanuel Latte Lath was also denied by Begovic 10 minutes later when he tried to beat him from a tight angle.
Smyth highlighted what danger he could pose when he worked his way into the area from the right and his low delivery across the six-yard box was crying out for Sinclair Armstrong to stretch to meet the ball, but it evaded him.
Another Smyth run caused panic in the home defence seconds before Dozzell found himself in loads of space 25 yards from goal. The midfielder’s thunderous drive crashed in off the left-hand post to put QPR ahead.
And in the sixth minute of stoppage time Begovic dived to his right to turn away a downward Darragh Lenihan header from Jonny Howson’s free-kick to keep the visitors in front.
After the restart frustrations started to grow for Middlesbrough.
Lath, who had already been denied by Begovic again, wasted a fantastic situation when Boro had a three-against-one on a counter-attack. QPR were gifted the ball, broke and Dieng prevented Sinclair from scoring at the other end.
Middlesbrough handed second-half appearances to new signings Sam Greenwood and Lewis O’Brien following loan moves from Leeds and Nottingham Forest respectively.
And Begovic was on hand once more to prevent Lath scoring after the striker linked up with Silvera in the penalty area on the hour.
Soon after a phantom whistle brought a short interruption in play, QPR had the important second goal.
Smyth again got to the line and beyond full-back Lukas Engel. His low cross led to Chair’s shot being blocked before former Newcastle and Sunderland midfielder Colback powered his drive into the net, and there was no way back for Boro after that.