The home side had deservedly led 10-3 at the break but a poor second half performance saw the Ravens edge it at the death.
Both teams scored two tries apiece, Neath moving ahead through a penalty try and a score from Dale Ford.
Bridgend's James Dixon had scored all of his side's points though it looked like it would be in vain with just seconds remaining.
But after some sustained late pressure, James dived over for Dixon to convert, leaving Langdon's missed kicks - two penalties and a conversion went awry - to prove costly.
Bridgend will now play either Swansea or Aberavon next weekend with the winners of that game progressing to the group stages of the competition proper.
After steady rain had cleared before kick-off, Langdon and Dixon exchanged early penalties in a quiet opening 20 minutes.
It was the home side who had more of the territory though and despite Langdon missing a second penalty chance, it wasn't long before Neath were back in front.
When the score came, it was a penalty try with the Neath pack rewarded for a solid start at scrum time. Langdon converted for a 10-3 lead though the Ravens could perhaps have felt aggrieved that they weren't warned at least once before the penalty try was given.
With a greasy ball, it was no surprise to see both sides making mistakes as a number of passes went to ground instead of their intended target. As a result, kicking became the order of day with Langdon and Bridgend's Jamie Murphy targeting the corners.
With the boot dominating the game, the likes of Ashley Evans and Bowdy Davies had little opportunity to showcase their skills and as a disappointing first half grew to a close, the only other action of note saw Langdon put another long range penalty effort wide.
The second half started in much the same fashion as the first before finally, the game sparked into life. Davies was the creator, a 60 metre break from inside his own half giving Neath a superb attacking platform. When the diminutive winger was finally scragged, Langdon spread the ball left for Ford to finish in the corner. Langdon missed the conversion but with a 12 point deficit and having created very little, Bridgend now had a mountain to climb.
Neath's second score seemed to spur Ben Rose's side into action though and just minutes after the restart, the Ravens were back in it. It was a scrappy try, Dixon hacking on a loose ball and winning a footrace to the line for a try he himself converted.
The score had given Bridgend a lifeline but just moments after the try, they were dealt a double blow. Openside Sam Treharne was stretchered with a nasty looking injury before replacement Owain Lloyd was yellow carded for an infringement at a ruck.
The injury delay hindered Bridgend's brief spell of momentum and with both sides then ringing the changes, the game reverted to stalemate.
Bridgend saw most of the ball and camped themselves in Neath's half though initially a second try failed to arrive.
But when Neath's Garyn Daniel was yellow carded for persistent infringement, Bridgend pounded away in attack and James pounced to send the Ravens home with the win.