The Dragons had failed to score in six of their previous seven meetings with Ireland before tonight, but they made up for lost time to give manager Ryan Giggs a perfect result in his first home match at the helm.
Goals from Tom Lawrence, Gareth Bale and Aaron Ramsey put Wales into a commanding lead at half time, and Connor Roberts added a fourth after the interval as the hosts began their UEFA Nations League campaign in convincing fashion.
Ireland did pull a goal back through Shaun Williams, but it was too little too late as their seven-match away unbeaten streak came to an emphatic end in the Welsh capital.
A second arrived only 11 minutes later, and this one was the pick of the bunch as the in-form Bale took a long pass down on his chest before cutting inside and bending an unstoppable strike into the top corner from the edge of the box.
Wales continued to dominate as the first half wore on in Cardiff, and Roberts almost added a third 10 minutes before the interval when he nodded narrowly over from Ben Davies's delivery.
Giggs would not have to wait too much longer for the third, though, with Ramsey all but wrapping up the game before half time when he tucked his finish past Randolph after being teed up by Ethan Ampadu.
The hosts looked in no mood to let up in the second half either, and Roberts made it four at the end of a sweeping team move when he collected Bale's pass on the edge of the box before drilling a low half-volley past Randolph at the near post.
There was one blot on the Welsh copybook shortly after the hour mark when a defensive error sent Williams clean through on goal, and the Millwall man kept his composure to dink a clever finish over Wayne Hennessey.
The comeback never looked likely, though, and Tyler Roberts almost restored the four-goal lead just four minutes after replacing Bale for his debut when he played a one-two with Ramsey before seeing his effort saved.
Wales comfortably saw out the victory to end their eight-match winless run against Ireland and gain a measure of revenge for their all-or-nothing World Cup qualifier defeat to the same opponents last year.
The result leaves Wales as the early leaders of League B Group Four in the UEFA Nations League ahead of their match against Denmark on Sunday. Ireland, meanwhile, will look to bounce back from this chastening defeat when they face Poland on Tuesday.
WALES (4-2-3-1): Hennessey; C Roberts, Williams, Mepham, Davies (Dummett 81'); Allen, Ampadu (Smith 67'); Lawrence, Ramsey, Brooks; Bale (T Roberts 75')
REPUBLIC OF IRELAND (4-4-2): Randolph; Coleman, Duffy, Clark, Ward (Stephens 61'); Christie, Hendrick, Hourihane (Williams 57'), O'Dowda; Walters, Robinson (Horgan 77')