Danny Hylton nodded in from close range two minutes into the second half before James Collins saw his half volley from the edge of the box beat keeper Craig Ross.
The victory saw the Hatters overtake Accrington at the summit of the fourth tier on goal difference, with results elsewhere meaning the Town are also eight points clear of fourth place.
Jones said: "It was an important win. The media have made a big thing about us not winning and getting draws and so on and so forth. I think we needed to shut a few people up and answer a few questions and we did.
"It was emphatic, it really was. We were outstanding, the way we moved the ball. It was all setup today for us to lose the game. Martin Allen coming back, live on Sky, but we were outstanding from start to finish.
"I keep saying to people, it's not easy to win games here. 4-4-1-1, they don't normally play like that. People don't normally play like that, but they do for us. I though we were excellent start to finish – we were brave and it could have been more.
"We didn't rest on our laurels (after the first goal) and we showed what a real good side we are because some teams that are struggling for wins will sit back and defend it but we didn't, we went for the second. We got the second, we should have had more and I am proud of them.
"We've had to dig deep and we've had some tough games, we've had some real tough games here, the Accrington result as I said, if it wasn't for the Accrington result it would have been a great month. A really, really good month. But others have made more of it and we've answered a few and that takes a lot of character and we have got bags of it."