The Dragons had suffered back-to-back defeats heading into Friday evening's showdown in South Wales, but three tries saw them recover in style to leave Ireland trailing England by three points after playing a game more.
Not since 2003 have Wales lost to England, Scotland and Ireland in a single campaign, though any chance of a repeat was eased by two George North tries inside the opening 44 minutes.
It was Ireland who got off the mark first thanks to a Jonny Sexton pen, but North crossed over for the first time soon after to give Wales a valuable lead.
Paddy Jackson took over kicking duties from head injury victim Sexton and found the target just short of the half-hour mark to swing the game back in his side's favour.
An unchanged Wales side upped the pressure as half time approached and were rewarded by a successful Leigh Halfpenny kick two minutes before the break, moments after Sexton was sent to the sin bin.
North's second try of the evening early in the second period put the Dragons on their way to a first win in three, which Halfpenny added to with the extras from close to the touchline.
A simple kick in front of the posts was never going to be missed by Sexton as the gap closed once again in the Welsh capital, and with 20 minutes on the clock a pivotal moment arrived.
The Irish maul was penalised just inches from the tryline, which proved to be the incentive Wales needed to push on and wrap up the win through Jamie Roberts - the Harlequins ace touching down following some good work from Taulupe Faletau.
All that was left was for Halfpenny to add two more points from his boot, with no bonus-point try arriving despite a late push, lifting Wales above Scotland into third place and seeing England installed as strong favourites to win successive crowns.