After a Round 2 scare against Italy, the hosts were back to their best with tries from Sean Edogbo, Hugh Gavin, Henry Walker, Sheahan (2) and Ben O’Connor making the difference.
Ieuan Davies scored Wales’ sole try but at 24-3 down it proved only a consolation, and the visitors have now suffered back-to-back defeats following their Round 2 loss against England.
Ireland travel to England in a mouth-watering Round 4 contest that could decide who wins the title, and head coach Richie Murphy will be pleased with how his team shaped up for that clash at the Rec.
On a still night that was perfect for rugby, Ireland fly-half Jack Murphy scored the first points of the match in the seventh minute with a penalty and the hosts soon had a man advantage too as Wales lost hooker Harry Thomas to the bin for an early yellow card
Harri Wilde levelled the score with a penalty of his own but Ireland dominated possession and territory and they broke through for their first try in the 18th minute when blindside flanker Edogbo powered over from close range.
Despite dominating large parts of the half, Ireland struggled to break through Wales’ defence and they had to wait until the stroke of half-time for Gavin to muscle his way over from a crash ball.
With a 14-point half-time advantage, Ireland relaxed after the break and re-discovered their fluency.
It took them just five minutes of the second half to score a third, as Walker dotted down, but Wales then scored their only try when Harri Ford picked the ball up inside his own and made a brilliant line-break before slipping a pass inside to Davies to sprint clear.
That was as good as it got for Wales, as replacement hooker Sheahan dotted down from the back of a roiling maul just after the hour mark.
He doubled his tally seven minutes later before O’Connor sprinted clear to score their sixth try following a fine break from Finn Treacy to wrap up a convincing win.