Wales had not beaten Ireland for 26 years and had scored only twice in their last seven meetings but ended that jinx with a spectacular opening 45 minutes in which Tom Lawrence and Aaron Ramsey scored either side of a classic Gareth Bale strike.
Connor Roberts made it 4-0 soon after the break and even Ireland's consolation scored by Shaun Williams was drowned out by a chorus of Welsh anthems echoing around the stadium.
In Giggs's first two matches in charge Wales have scored 10 times after he began his reign with a 6-0 victory in China.
Playing with the kind of pace and verve Giggs was noted for throughout his illustrious Manchester United career, Wales tore Martin O'Neill's sorry Ireland side to shreds.
Lawrence opened the scoring after six minutes, rifling a low shot past Ireland goalkeeper Darren Randolph after being played in by Joe Allen at the end of a sweeping move.
Twelve minutes later it was 2-0 as Bale took a long Ben Davies pass on his chest before cutting in from the right and curling a left-footed beauty beyond Randolph.
Wales continued to dominate and scored again in the 37th minute as 17-year-old Chelsea midfielder Ethan Ampadu surged forward and played a perfect pass for Aaron Ramsey to finish inside the near post.
Roberts volleyed in from 20 metres for the fourth goal before a defensive mistake -- the one blip on a night of Welsh joy -- allowed Williams to salvage a little Irish pride.
Denmark are also in League B, Group 4 along with Wales and Ireland. Wales face Denmark away on Sunday.
(Reporting by Martyn Herman; editing by Ken Ferris)
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