Efforts from Paul McVeigh and Chris Martin in a scintillating first 25 minutes for the hosts left the Hatters in control.
The Bees struck back through Abu Ogogo before the break, but Ogogo was then sent off for a second bookable offence as the teams left the pitch at half-time.
Michael Spillane and McVeigh both hit the woodwork as the home side bossed the second period, before Michael Townsend's late own goal sealed the win.
The result left the visitors without a win in their last ten matches.
Luton started the brighter and almost went ahead when McVeigh found Martin, who cut inside from the left past Ogogo and fired in a low effort that was blocked by the legs of the visitors' ex-Hatters keeper Rob Beckwith.
The hosts continued to press and took the lead in fine style three minutes later. Kevin Gallen was first to a long clearance from Conrad Logan and laid off for Martin to roll the ball to McVeigh, who sidefooted into the top corner of the net from 18 yards for an assured finish.
After quarter of an hour it was 2-0 as Martin rose to glance home Rossi Jarvis' free-kick from the right, sending the ball nestling into the far corner of the net.
Gallen almost grabbed a third two minutes later as his 20-yard free-kick whistled past the post and 60 seconds on only a fingertip save by Beckwith caused McVeigh's 30-yard volley to divert over the crossbar.
The one-way traffic continued as McVeigh - revelling in his new role behind the front two - chipped in for Talbot to blaze over from just three yards out in the 21st minute.
Barnet were being run ragged and responded by bringing on Max Porter for Adam Burchall in the 24th minute and that signalled a change in the nature of the game.
Albert Adomah registered the Bees' first shot on target in the 34th minute as Logan saved and the Town goalkeeper then had to smother at the feet of John O'Flynn two minutes later after the striker's neat turn in the penalty area.
Five minutes before the break Barnet were back in it as Kenny Gillet made progress down the left and fired in a low cross which was turned home by Ogogo from six yards out.
However, drama after the half-time whistle saw goalscorer Ogogo turn from hero to villain as he reacted to a challenge from Martin and was sent off for a second bookable offence.
Luton made their extra man count after the interval as George Pilkington headed just wide from eight yards after Jarvis' 53rd minute corner and two minutes later Spillane ended a marauding run into the penalty area with an angled drive that was pushed on to the post by Beckwith.
Despite having plenty of possession, the Hatters were restricted to half-chances then on and Beckwith was next called into action to push aside McVeigh's 25-yard effort in the 79th minute.
Three minutes from time Beckwth denied McVeigh again as he tipped the Irishman's free-kick on to the crossbar.
However, Beckwith was beaten a minute later as Towsend diverted man-of-the-match McVeigh's cross into his own net.