In what was their 300th fixture in the top flight of English football, the Bees had to be patient against a rigid Luton rearguard, but strikes from Neal Maupay, Ben Mee and Shandon Baptiste rendered Jacob Brown's second goal in as many weeks inconsequential.
Brentford's full-back crisis worsened ahead of kickoff, as Kristoffer Ajer was a late withdrawal from the XI owing to a rolled ankle in the warmup - Saman Ghoddos was introduced having originally lost his place to Maupay.
Luton's own full-back ranks were also hit by the absence of Alfie Doughty through a knock, although Issa Kabore's return from a concussion softened that blow, and the Hatters also had to survive an early scare to Tom Lockyer, who took a knee in the back from Christian Norgaard but was able to shake it off.
Thomas Frank's men unsurprisingly saw the majority of the ball in the earliest exchanges, but the Hatters shielded Thomas Kaminski exceptionally well; the Luton number one did not have a save to make until he plucked a Maupay header out of the air in the 21st minute.
The Cameroonian - who was still looking the Bees' most dangerous player - would cut inside again in the 37th minute, only to see his shot deflected just wide of the far post, one moment before Kaminski went into Anthony Taylor's book for timewasting.
The hosts upped the ante as the half drew to a close, as Yoane Wissa created the angle for a chance in the 39th minute, which Kaminski gathered at the second attempt, and Luton survived a late handball appeal against Kabore to enter the break on level terms.
However, the visitors were dealt a significant blow as the teams went into the tunnel, as Lockyer stayed down in the penalty area with an injury before limping off, and Rob Edwards was forced to replace his skipper with Brown, who took up a right wing-back role.
After holding out admirably in the first half, Luton's resistance was broken four minutes into the second, as Mee failed to connect with Wissa's ball into the box, but Maupay was on hand to feed off the scraps.
The galvanised Bees smelled blood, as Frank Onyeka curled just over from inside the D in the 54th minute, and only two moments later, the hosts doubled their advantage from yet another cross.
An Mbeumo corner was on the money for an unmarked Mee, whose header took a wicked deflection off Carlton Morris and wrong-footed Kaminski, giving the Bees a merited two-goal cushion heading into the final half-hour.
While the Bees looked the more likely to score again, they were caught cold in the freezing cold in the 76th minute, as Ross Barkley played a sublime defence-splitting pass through to substitute Brown, who cut inside and clinically finished low into Mark Flekken's goal to give the Hatters hope.
That hope was firmly extinguished in the 82nd minute, as the lively Keane Lewis-Potter had two shots blocked and one saved inside the box, but the rebound from the latter fell kindly for Baptiste to restore the hosts' two-goal cushion.
Just before eight minutes of added time went up on the fourth official's board, Tahith Chong headed an Andros Townsend cross into the back of the net, but the offside flag denied the Luton attacker as Brentford celebrated a return to victorious ways.
Frank's men have risen back above West London rivals Chelsea into 10th spot in the table courtesy of Saturday's victory, whereas Luton - who are still without a clean sheet in the top flight this term - remain 17th.
Brentford now have a trip to Brighton & Hove Albion pencilled in for Wednesday night, while Luton host title-chasing Arsenal on Tuesday. body check tags ::