Story of the match
It was the latter, who had the first real opportunity of the game, when the Spaniard tried his luck from the edge of the box, forcing Simon Sluga to tip over in acrobatic fashion.
In the 14th minute, Saman Ghoddos nodded the hosts into the lead, heading home Ivan Toney's excellent first-time cross from the wide right.
Canos nearly made it two just six minutes later, firing his effort straight at Sluga, after he head cut in from the left flank.
The Hatters best chance of the half fell to Pelly Ruddock Mpnazu, winning the ball just outside Brentford's area and firing the subsequent shot over the bar.
Luton picked up where they left off at the start of the second half, with The Hatters putting some dangerous balls into the box.
In the 54th minute, Brentford goalkeeper David Raya made a vital interception to stop James Collins tapping in an equaliser from Mpanzu's lofted ball into the box.
Brentford had to endure long spells of Luton pressure in the first 15 minutes of the second half, but showed just how dangerous they are on the counter attack, when Toney saw his effort saved by the feet of Sluga after a swift Bees move.
Luton made a triple substitution 20 minutes into the second 45 and continued to dominate in-form Bees. Kazenga LuaLua - being one of those substitutes - took just a minute to make an impact when he won possession out wide before delivering a cross that was met by Cornick, who was unable to divert the ball beyond Raya in the Brentford net.
In the 75th minute, another one of the three substitutes Jordan Clark nearly grabbed the all-important equaliser, but the winger dragged his effort wide after a brilliant first touch from James Bree's cross.
Three minutes later, Ryan Tunnicliffe saw his improvised effort lob Raya, but the Spanish keeper dived back in spectacular fashion to prevent the equaliser.
In the 88th minute, Mathias Jensen thought he had doubled Brentford's advantage, when the midfielder drove into the box, chipping the ball over the onrushing Sluga, but the ball bounced agonisingly wide.
With less than a minute to go, an incident between Ivan Toney and Tom Lockyer led to the pair being sent off.
Brentford extend their unbeaten run to 16
It might not have been the best Brentford performance in recent times, but they ultimately hung on for all three points. They move into third position and if they win their game in hand, they will see themselves in second.
A game of two halves
Brentford dominated the opening exchanges and were perhaps unlucky not to be two goals in front after 30 minutes. Luton grew into the game from then on, but they ultimately could not find the goal that their pressure warranted.
The eventual match winner Saman Ghoddos particularly stood out. Not only has the 27-year-old had to work extremely hard to gain a place in Thomas Frank’s side, but he has also had to adapt to a more central role. In the first half, everything Brentford did came through the Iranian international who linked up the play brilliantly. He made a great driving run to get on the end of Toney’s first time cross for the only goal of the game.
Once again, Kiernan Dewsbury-Hall stood out for the visitors. The Leicester City loanee picked up possession in threatening positions and looked to go forward at every given opportunity. He linked up well with his wingers and James Collins and was unlucky not to register an assist on a couple of occasions.