After Bradley Davies' sinbinning, Tommy Bowe's try had put Ireland in the box seat before George North's score brought Wales to within a point of the hosts.
Although Leigh Halfpenny failed to convert North's try he made no mistake second time around when Stephen Ferris conceded a penalty in the dying seconds.
And Jones admits the match will live long his memory.
"What a wonderful advert for RBS 6 Nations rugby, with two teams going at it hammer and tongs and the game won in the last 20 seconds," he said.
"The drama was special and it was a great afternoon.
"And it was played in a great arena. We hadn't been to the Aviva Stadium before and didn't train here the day beforehand, like we usually do.
"To walk out into an atmosphere like that was wonderful, with all the green flags in the lower tier. The ground seemed to keep the noise in.
"That's what fantastic sporting occasions are all about.
"It meant so much to be on the right end of a result like that. We seem to have been on the wrong end a few times."
"You can talk about confidence and momentum, but this competition is about one game at a time. They are wonderful encounters and there's a lot of history around all these Test matches. That's what makes the Six Nations different from any other competition.
"The competition is still wide open. But we've put ourselves in a good position. We are in still control of our own future, which is where you want to be going into the next few fixtures."
With three home fixtures to come for Wales, the possibility of a first Grand Slam since 2008 has been raised by supporters.
And while Jones was delighted by the team spirit shown after Davies was yellow carded, he maintains there are plenty of areas for improvement, particularly in the set piece.
"We dug deep when Brad went off," said Jones. "That was the spirit we showed in the World Cup and we've managed to carry that on and have come away with a wonderful result.
"Grand Slams do start with a victory, I suppose, and we are in control of our own destiny.
"It was the start we so dearly needed and it bodes well but it was by no means a complete performance.
"There will be lots of finger pointing and we'll tear apart the game, looking at areas of concerns and weakness we perceive that we have and build on them.
"We're always looking to improve - and it is a competition where the team will develop as it goes on.
"It is not about resting on your laurels, it is about building on the confidence we've gained from this."