The Bees showed no derby day nerves and started on the front foot. Liam Kelly was forced into an early save with Ethan Pinnock glancing a header off the crossbar from the resulting corner. QPR had offered little going forward but, when they did, they got hit ruthlessly on the counter.
Bryan Mbeumo won the ball back on the edge of our own box and hit a long ball forward for Ollie Watkins. The frontman drove down the right wing and then crossed for the on-rushing Christian Norgaard to power home.
In the aftermath of the goal, the two sides traded effort; Bright Osayi-Samuel shooting straight at David Raya from a good position before Mbeumo's header brought a regulation save out of Kelly.
Mbeumo shot wide a couple of minutes later from a good position before Sam Jacques' side grabbed their second. A long Henrik Dalsgaard throw was met at the front post by Said Benrahma and he flicked a header into the back of the net.
Rico Henry had a chance to settle it straight after but he couldn't find the finish after a lung-bursting run forward. Moments later QPR were awarded a lifeline as Pontus Jansson felled Ebere Eze in the box; the Rangers' forward saw his initial effort come back off the post before he buried the rebound.
One could have become two for QPR instantly but Raya stood up well to beat away Jordan Hugill's shot.
Jacques was dealt a blow just before the break losing Benrahma to injury and another one early in the second-half as Jansson was also forced off.
Chances were more at a premium during the second-half. Pinnock nodded wide of the near post while at the other end Ilias Chair headed over from 12 yards.
Any late nerves were settled in the final minute as Emiliano Marcondes slammed home his second penalty in as many games after another long Dalsgaard throw has caused confusion at the back. Sergi Canos could have made it four in the dying seconds but Ryan Manning timed his challenge to perfection just as the Spaniard was about to shoot.
The win sees Sam into the Last Eight where he is joined by Preston North End, Huddersfield Town and Birmingham City.
The rest of the week's action sees Middlesbrough host Bolton Wanderers, Nottingham Forest face Mansfield Town, Wycombe Wanderers travel to Fulham, and Swansea City entertain Wigan Athletic.
As well as supporting The Bees during the tournament, you can also show your support for the EFL’s charity partner, Mind, the mental health charity. In these tough times their services are needed more than ever so while you’re being entertained by the action, please consider donating on this JustGiving page which will be open during the tournament.