In the standings Welsh ahead of Ireland by one point, and as much behind Serbia.
Wales controlled the ball and Ireland only got a chance to get the ball forward when Allen was booked for a swipe at Meyler's legs.
Former Leicester, Aston Villa and Celtic manager O'Neill, meanwhile, revelled in his side upsetting the odds and emerging from a group which he considered one of the most perilous.
After hassling and harrying the Welsh defense, the Burnley midfielder fired in a low cross that Harry Arter did brilliantly to stepover. "We had to withstand pressure as you expect but we knew at some stage we had to win the match, and we did it". This group of players have made the difference. I don't think we'd want to play Portugal and there are six others I'd rather not, too.
Serbia sits in first place on 18 points, while Wales has 17 and Ireland has 16.
Coleman's side consequently finished third in Group D, with Ireland advancing to the play-off stage behind Serbia following James McClean's second-half victor.
"Unbelievable. There's no better feeling", said goalscorer McLean. "It was by far my best [international goal]", admitted McClean after the Derry man put Martin O'Neill's team within two games of next summer's World Cup finals in Russian Federation.
McClean hopes that Ireland can build on a huge win and come out on top against whoever they face in the play-offs. We'll go and attack, go and score goals.
"But we showed our character and our quality".
I can't overstate my admiration for the determination of the players in this game.
"Michael O'Neill and his players continue to make history with their incredible performances and results, while the fans have been true ambassadors off the pitch".
But victory over Martin O'Neill's side all but ensures they progress to the second round.
"James has just been magnificent for us".
A win will secure a playoff spot for Wales and could earn them a spot in Russian Federation if results between Serbia and Georgia go their way.
The last half-hour seemed like an eternity to me, to be perfectly honest.
"To be here now is an absolute joy for me".