The Hatters had got through to half time unscathed, before falling 2-0 behind as Neal Maupay and Ben Mee scored.
Sub Jacob Brown pulled one back on 76 minutes only for Shandon Baptiste to seal victory and to find out how the Town players rated on the afternoon, see below.
13. Jordan Clark (SUB): 6
One of three brought on with an hour gone as Town boss Edwards looked to try and get something out of the game despite being 2-0 down. Early cross into Adebayo led to a chance, as Luton went on to pull one back 15 minutes later, but those hopes of an equaliser went as they were undone at the back soon afterwards. Photo: Liam Smith
14. Elijah Adebayo (SUB): 6
Helped hold the ball up well for the final half an hour, one chest down for Brown to lash a shot wide as he looked to try and counter when possible for the visitors. With such a hectic schedule this month, could well push Morris for a starting place in the next few weeks. Photo: Liam Smith
15. Andros Townsend (SUB): 6.5
Winger tried to get forward and force the issue as Luton had more of a presence higher up the pitch in the closing stages. Looked like he had one done that when sending over a perfect cross for Chong to find the net, but unfortunately his team-mate had gone just too early and the goal was disallowed. Photo: Liam Smith
16. Ryan Giles (SUB): 6
After surprisingly not coming on at the break to replace the injured Lockyer, he was eventually introduced for the final 15 minutes when Mengi was off. Tried to help out on the left but saw his crosses more often than not cleared away by Brentford. Photo: Liam Smith