Carl McHugh's thumping header in the second minute of injury time proved enough to secure a morale-boosting win for Phil Parkinson's men in front of boisterous home crowd at the Coral Windows Stadium.
After drawing eight of their previous thirteen league games, the welcome Vale victory was City's first since the end of November.
As City dominated their contest with Vale looking for the vital break-through, the Bantams followers were in full voice throughout to make for a cracking night-time atmosphere.
Jones knows that the supporters have had to ensure some frustrating times in recent months as the club looked to get back to winning ways, and the Bantams captain wanted to personally thank the fans for their tremendous support on Tuesday night.
Jones said:"I'd just like to give a special mention to the fans really.
"I thought they were unbelievable throughout the match on Tuesday.
"We know that the fans will have been frustrated a bit in recent times but they didn't show it last night (Tuesday).
"They were incredible. They got right behind us and sang throughout the match.
"The lads were so grateful for the backing we received from the fans.
"It was brilliant to get the win and send them (the fans) home happy.
"We have truly incredible supporters here. As I've said before, they are some of the best around.
"The way they get behind us is frightening. We've had this dodgy spell of late but they never stopped believing in us and getting behind us.
"Hopefully now we can get on a bit of a good run for ourselves and themselves."
It was Jones, of course, who was the player on hand to set-up McHugh's all-important match-winner as the skipper's corner gave the Irishman the opportunity to power home his late thumping header.
The Bantams captain added: "It was such a relief to see it go in.
"It seem to take an age to drop in but it was such an amazing feeling when it did.
"We should definitely take a lot of confidence from Tuesday night. From the performance as well as the result really.
"Port Vale are just outside the Play-Offs and I felt we were the better side from start to finish."