Top scorer James Collins was to prove the hero, coming off the bench to score with his first touch from the penalty spot with 12 minutes left, and dent the Hornets' bid for promotion back to the Premier League.
Jones said: "That was a big, significant win, but what a thoroughly deserved win, a wonderful performance from start to finish as it was deserved.
"We were totally dominant in that game, probably as dominant a performance as we've ever had here, I'm so, so delighted.
"I want to dedicate that to Gary Sweet (chief executive), to the 2020 consortium for the work they've done and also our fans, because I know how much that means to everyone here.
"A big win, a win against your rivals and we've waited quite a long time, it's 15 years since they've played this game, and we've been at different levels for 15 years.
"Now we're at the same level, I don't know how long for, but all we can do is play who is in front of us and I think we were absolutely magnificent, I'm so proud of the group, the club, everything.
"We should have been further ahead, if there were fans here, that could have been four, five or six, you just never know, but I think the level of performance was outstanding.
"They are a top side and they should be as they are ex-Premier League and so on, but today, they got dominated by a wonderful Luton team and I'm so proud of that."
The Hatters dominated the first period, going close on a number of occasions, Luke Berry's early volley easy for Bachmann.
The striker was injured in the challenge, as Collins came on to slot home the penalty with his first touch, before Watford thought they had a leveller in stoppage time, only for ex-Luton forward Andre Gray to be ruled offside.
Hornets head coach Xisco Munoz said: "It was not our best performance and we know about this.
"It's important that we need to stay together. Now is the moment we need to stay together, everyone, and now it's important everyone puts more passion into our club.
"It's my job to try to get everyone one step in front. My team tried to give their best today. We know today is a very difficult game because we have a different situation and it was not our performance.
"Now we prepare the maximum for the next game because it's important."
"We play a lot of games, we have a lot of things happen, we have international players in the squad and many different moments.
"We have 24 players or 25 players ready to play and it doesn't matter who plays or not. I don't want to make excuses."