Earlier, the smallest man on the field, Shane Williams, opened the scoring in only the third minute when he crashed over in the right-hand corner.
Priestland slotted the sideline conversion to the delight of the Welsh supporters, who were clearly outnumbered in volume and voice by the travelling Irish fans.
Ireland turned down early opportunities to take shots at goal when Wales infringed at the ruck.
The Dragons defended like men possessed during the opening 20 minutes and were particularly efficient in their own 22-metre area, as Ireland had plenty of ball.
Eventually, Ireland gave in to temptation and Ronan O'Gara, who was playing his 118th international, put the Green Machine on the board in the 24th minute with a penalty goal.
With the wind at their backs in the opening spell, O'Gara kicked for position and tried to turn the youthful Welsh backline around.
Welsh fullback Leigh Halfpenny defied the swirling winds to boot an extraordinary long-range penalty goal in the 29th minute to extend the Dragons' early advantage.
Ireland captain Brian O'Driscoll equalled the Irish record for the most test matches against Wales, with 14 appearances, and he was busy throughout the game with his direct running in the midfield.
O'Gara might not have had the sharpest of first halves, but he provided a vital conversion early in the second spell after Irish winger Keith Earls bagged a controversial five-pointer in the 45th minute.
Earls received the ball in open real estate near the line and scampered to the chalk and his foot looked like it may have touched the sideline, but the TMO gave referee Craig Joubert the all clear to award the score.
The try gave Ireland hope, with the scores level at 10-all.
But, Welsh scrumhalf Mike Phillips took the opportunity to exploit a vacant blindside, when he dotted down from close range in the 51st minute, which restored the Welsh lead.
With 25 minutes to play, O'Gara and halfback Conor Murray were yanked from the pitch and replaced by Jonathan Sexton and Eoin Reddan, respectively but they failed to spark their backline.
Wales on the other hand offered a lot more in attack and will meet either England or France in the next round.
The match marked the 117th time the two sides have played against each other and was only their third clash at a World Cup.
Wales 22 (Shane Williams, Mike Phillips, Jonathan Davies tries; Rhys Priestland 2 conversions, Leigh Halfpenny penalty) def. Ireland 10 (Keith Earls try; Ronan O'Gara conversion, penalty). HT: 10-3.
MATCH RECAP:
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