Andrew Shinnie notched his first league goal of the season with an outstanding curling finish in the 19th minute, with Dan Potts heading in his fifth goal of the campaign with 30 minutes on the clock to give the Town a 2-0 lead going in at the break.
Substitute Harry Cornick got his second in a Town shirt when he finished off a superb counter in the 76th minute, before Danny Hylton missed the opportunity to add to the lead when Jack Bonham dived to his left to save the striker's penalty after he had been upended by Clint Hill.
The result sees the Hatters move up to the top of League Two on goal difference, after Notts County were held to a drew at Yeovil Town.
Jones said: "[It was] brilliant, absolutely brilliant. Especially the manner of the win as well. Carlisle come here unbeaten in six, in real good form. They have got real good players, experienced at the level – know how to play the game.
"It was a brilliant first half, we score a wonderful goal through Andrew Shinnie, then score another from a set-play, so we go in two up.
"We knew that they would change and we had to weather a bit of play, fair play to Carlisle, they came out in the second half and gave it their all. When teams do that we know we have got a counterattacking threat and we did that. Harry Cornick did that. It was brilliant for him to get a goal. A real good performance and great to be back at the top.
"Last year we drew both games against Carlisle and they had similar aspirations to us, and they have them this season as well.
"They have got good experience. People like Clint Hill, Liddle, Grainger – real experience at the level. So to beat them 3-0 at home, it didn't flatter us in anyway and I thought we were excellent, I really did.
"The manner of it after winning by seven at home on the weekend to come here and do that, it was a professional performance. Two clean sheets and ten goals in a week is absolutely wonderful. I am delighted, I really am."