Wayne Pivac’s side downed a 14-man Irish team who lost flanker Peter O’Mahony to a red card thanks to tries from George North and Louis Rees-Zammit.
Scarlets loosehead prop Jones was man of the match at Principality Stadium.
Now he and his team-mates are preparing for a trip to Edinburgh where they will face a Scotland side who claimed a famous win over England at Twickenham in round one.
Jones said: “I think that was only the second man of the match of my career with the first one against the Barbarians! It’s always nice for a prop to get it and I am chuffed.
“We always knew it would be a tough game. If you win the first game and get a bit of momentum behind you in this competition you’re always in the running towards the end.
“We’re happy for the win and we move on to next week now. Scotland showed they were a very good side on Saturday. They took their chances, defended well, and were deserved winners.
“We know what threats Scotland bring and we know that from the autumn. We look forward to that game. As this is the Six Nations, there is more at stake. We’ll try and right the wrongs of last time.”
Wales have only a six-day turnaround between facing Ireland and Scotland.
Head coach Pivac will have Liam Williams back available to face Scotland after he served his suspension for a red card when playing for Scarlets against Cardiff Blues.
“Liam is always buzzing and wants to play,” said Jones, who plays with Williams at the Scarlets.
“I’m sure he would have been frustrated watching the Ireland game and wanting to play.
“Unfortunately, he was banned but it’s nice to have him back and we will see how he goes.”
