It was meant to be the beginning of a new era for Gary Speed but his first game in charge ended in almost typical Welsh disappointment on a dreary Dublin night.
After a nondescript opening half, Gibson opened the scoring in the 60th minute with his first international goal before Damien Duff doubled the home side's lead six minutes later from close range.
As the Irish took a firmer grip, substitute Keith Fahey drove a 25-yard free-kick past Wales goalkeeper Wayne Hennessey to compound Speed's misery, although long before that he would have known the task which confronts him.
Republic boss Giovanni Trapattoni handed Seamus Coleman and Ciaran Clark their first caps, while Speed included Reading's Hal Robson-Kanu in a three-man attack which failed to make much of an impact.
Stoke midfielder Glenn Whelan had the tournament's first effort on goal after two minutes, but his delicate chip from the edge of the box cleared the bar.
Moments later Duff came closer with curling effort from the left which almost deceived Hennessey and appeared to clip the woodwork before going wide, but a decent start soon subsided and there was little in the way of Celtic passion.
Wales, conservative and constrained, grew in confidence as they slowly felt their way into the game, but there was still no clear-cut chance at either end.
In the 25th minute Robson-Kanu played a one-two with Andy King and then appealed for a penalty as he went down under pressure from John O'Shea as he tried to reach the return ball, but Northern Irish referee Mark Courtney was unimpressed.
On the half-hour mark Robert Earnshaw was fouled clumsily by Clark 25 yards from goal but the Wales striker drove the resultant free-kick over the bar.
Five minutes later Doyle threatened for the first time when he drove at the Wales box before unleashing a low drive from 20 yards, but Hennessey just stood his ground and gathered.
Moments later Coleman took a free-kick from Gibson and lifted the ball into the box where Clark rose to head inches past the post from 12 yards.
Seconds before the interval Wales striker Simon Church linked up well with Earnshaw and his left-footed drive from outside the box had Shay Given happy to gather at the second attempt.
Chris Gunter came on for Neal Eardley for the start of the second half and Reading striker Shane Long replaced Doyle.
The second half was only four minutes old when Jonathan Walters fired in a drive from the edge of the box but again Hennessey was perfectly placed to gather.
Moments later Long had the chance to make a quick impact when he was set up by Duff 16 yards out, but blazed the ball over the bar.
The game was then held up when two spectators ran onto the park, but once they had been removed by the stewards Ireland regained the ascendancy and in the 56th minute Hennessey made a good block from Duff's close-range shot, although the Fulham player looked to have lost his balance as he shot from 12 yards.
The deadlock was eventually broken on the hour mark and in some style when Gibson picked up a pass from Whelan before rifling an unstoppable shot from 20 yards high past Hennessey, who this time had no chance.
Duff made it 2-0 in the 66th minute after Gunter had carelessly been robbed by Walters on the byline.
The cutback was missed by Long and landed at the feet of former Chelsea and Newcastle player Duff and he buried it from 10 yards out.
The game appeared over as a contest but it became increasingly disjointed as both sides rang the changes.
In the 82nd minute, after Walters had been fouled by Collins 25 yards from goal, Fahey - on earlier for Coleman - drove the free-kick past the helpless Hennessey to confirm a good night's work.
However, on this evidence Speed has his work cut out to get this Wales side knocked into shape.