The defeat was a significant blow to the Welsh side's hopes of automatic qualification to next season's European showpiece tournament.
If the Italians are beaten in Dublin, victory against Cyprus in Parma next Wednesday will ensure top spot and automatic qualification for Lippi's side.
Slovenia defeated group leaders Slovakia 2-0 and the two are now vying for the one automatic qualification spot, with the other entering the play-offs.
Italy will secure their place in the finals if they draw while the Republic will put themselves in with a chance of automatic qualification if they win.
The Scarlets sit a point above the Dragons with a game in hand, knowing one win will be enough for automatic qualification to European club rugby's top table.
Portugal's hopes of automatic qualification from Group F suffered a big blow as Cristiano Ronaldo's team needed late goals from Helder Postiga and Fabio Coentrao to draw 3-3 in Israel.
We limited consideration to schools in the major conferences that compete for automatic qualification to the five Bowl Championship Series bowl games: the ACC, Big East, Big Ten, Big 12, Pac-12 and SEC.
In Group Two, leaders Switzerland took a step closer to automatic qualification with a 3-0 victory in Luxembourg, as defender Philippe Senderos scored twice before Benjamin Huggel also netted in the 22nd minute.
Garcia's position on the World and European points lists are not currently high enough to secure automatic qualification, though if his ranking did not improve he would be a strong candidate for a wildcard slot.
We looked at members of the ACC, Big East, Big Ten, Big 12, Pac-12 and SEC because those schools are eligible for an automatic qualification to a Bowl Championship Series bowl game (Fiesta, Orange, Rose, and Sugar Bowls).
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