James Collins scored his 50th goal for the club, while Matty Pearson netted on his return to side where he started his career, as the Hatters climbed to 16th in the table.
Although Rovers had 66 per cent of the possession and 16 attempts, crucially only two of them were on target, as the visitors resolutely defended their goal, throwing their bodies on the line to prevent keeper Simon Sluga having a great deal to do.
Speaking afterwards, Jones said: “We had to defend our way to victory today, we didn’t attack our way to victory, we defended our way and the character of the boys, the understanding of the boys was excellent.
“Irrespective of the result, we needed to be competitive again.
“I think the last seven uminutes against Hull damaged us as it’s not a way to lose a football match.
“Leicester was a one off occasion really, but on Thursday, I was brutally honest with the boys.
“I asked for the same mental and physical consistency during the game, no matter what the scoreline is and I told them if we get that we’ll win the game.
“We played in a different way today, we used bits of the Leicester game to help us and we showed great character and came out 2-1 winners.”
It had looked like Luton were in for a long afternoon during the opening stages as Rovers dominated both possession and territory.
Vitally, they couldn’t breach the Hatters back-line though, as Jones said: “If you watch Blackburn for the first 20 minutes, you felt their quality.
“I didn’t want to come into the game and start being negative, I knew we had to be absolutely at our best.
“I knew set-pieces would be important in order for us to win here, they are a really, really strong Championship side, so for us to come here and do what we did was really, really satisfying.”
For the final half hour, Town had to defend against some high class players, Danny Graham and former German international Lewis Holtby on, but they did so impressively.
Jones added: “We changed the shape because you can feel Danny Graham’s threat and they put two up front, three up front, four up front, they’re throwing it in the box.
“We won the game 2-1, we conceded one goal, all I asked for the other day was to win the game, we got that and I’m extremely happy.
“We were absolutely in the game, we controlled the game defensively, not on the ball, possession stats were down, but that was set up that way.”