Brian O'Driscoll said Ireland had "owed Wales one" after the visitors withstood a second-half comeback in Cardiff.
O'Driscoll, replaced as skipper by Jamie Heaslip before the Championship, was among Ireland's try-scorers as Declan Kidney's side won 30-22.
"The first game is a must-win," said man of the match O'Driscoll.
"Otherwise you are chasing your tail for the rest of the Championship. We started really well today."
O'Driscoll's magnificent pass set up Simon Zebo's first Irish try and Cian Healy's touchdown helped extend Ireland's lead to 23-3 at the interval.
The former skipper scrambled over a third Irish try early in the second half which proved vital as Wales summoned up a battling comeback to dominate the remainder of the contest.
O'Driscoll added: "They have done a job on us the last three times [we have met].
"We came out of the blocks in the first half and played really well.
"They weren't going to be flat for the whole game and put it up to us in the second half.
"They were able to kick to the corners and build. They tied us down and got on the front foot."
Ireland coach Declan Kidney heaped praise on his former skipper's display.
"He was brilliant but that's Brian," said the Ireland coach, who may need his team to produce a successful Six Nations to have any chance of his contract being extended.
Kidney's decision to remove the captaincy from O'Driscoll was a major surprise and the Lions centre responded by producing another tremendous display in the green shirt.
"Like we said, we wanted Brian the player as much as Brian the captain and he was just brilliant today," added the Ireland coach, whose current deal runs out in the summer.
Kidney was typically measured in his assessment of his team's display.
"Obviously, with the first half we'd be delighted and with the second half, we'd be needing to take a good look at it.
"We did (have to defend with our lives) but that's when a group really comes together.
"You can't practice what they did out there (in terms of defence) but I would like to believe that will give them a lot of confidence in how they played for one another.
"Guys didn't care about themselves today. They just put themselves where they needed to be.
"The first half was pretty good.
"I saw Rob (Kearney) talking before the game about thin margins. Rory (Best) got a good block-down (for the second try) and managed to gather the ball.
"Three passes then went to hand and we were in for a try. Those small margins makes a massive difference."