Having been in control of the match from the off, the Bees secured victory late on through substitute Karleigh Osborne and Adam Newton.
Luton will feel aggrieved with the handball decision given in the build-up to the opening goal, but will accept their defending was not up to scratch as Osborne nodded home Moses Ademola's cross in the crowded area.
And as the league's bottom side pushed forward in the closing stages, Newton wrapped up proceedings with a brilliant left-footed curling effort that eluded Dean Brill.
But in truth it was a game that Brentford should have won by more goals as they failed to convert the chances that came to them - particularly in the first half.
It took the hosts just five minutes to record their first effort, when on-loan striker Billy Clarke headed Sam Wood's right-wing cross over the bar.
On the half-hour mark the industrious Sam Williams played a perfect knockdown for Wood, who saw his crisp half-volley lack sufficient power to properly test Brill.
The Bees created their best chance of the half just five minutes later after a series of quick passes carved open the right side of Luton's defence. But Brill was at his best to stop another Clarke effort low down to his right.
The second half was bereft of any real clear-cut opportunities until Osborne made the breakthrough in the 73rd minute and Newton put the result beyond doubt with just a minute to play.
Brentford will be delighted with the win, but not by the actions of their supporters who invaded the pitch with the game barely over - which saw a massive police presence required.