Wayne Rooney opened the scoring with a deflected effort in the second half, before goals from Pelly-Ruddock Mpanzu and Donervon Daniels put the Hatters in front.
Chris Martin equalised with a header, before Harry Cornick’s effort was put into the back of the Derby net by Rams defender Jayden Bogle to secure the three points for Town.
Jones said: “I think before the game we knew we had to find a way of getting a positive result – that meant a draw or a win. But I felt it coming with the performance at Nottingham Forest, I think it’s our first win in nine maybe. We got a draw against Fulham.
“It was incredibly satisfying, because we have managed to stay together when everybody has tried to divide us and they haven’t. Against all odds, to respond to going a goal down is really satisfying.
“[I was most satisfied with] the desire, the need, the character of the group – I think we had more efforts on target than them. They had more possession, they have got some really good players, you look at Chris Martin and Jack Marriott coming off the bench, it shows you the level that we are at. But our lads didn’t listen to any of that.
“I saw it at Forest where they know they can play at this level and it’s not easy and you have got to be in every phase of play.
"Tonight I thought we were exceptional in terms of off the ball. On the ball we still managed to have that composure, that confidence and that belief to play when confidence is low, you’re under pressure and you’ve got to play and you’ve got to get results, you’re bottom of the league. We learned our lessons from Birmingham, that’s satisfying as well.”