Mike Ruddock's youngsters, who are now second in Pool B with six points, have their destiny in their own hands after picking up bonus points in the 19-13 defeat to France and their four-try victory over the Welsh.
Tournament hosts New Zealand and Australia are second in their respective pools on five points each, so Ireland hold a slight edge as the teams compete for the last-four spots.
Unbeaten pool leaders England, South Africa and France are currently on course to reach the semi-finals, with 10, 10 and 9 points respectively.
Delighted with the result against Wales, Ireland U-20 captain Jack O'Donoghue said afterwards: "We are absolutely thrilled, things didn't go our way against France but we surely put them right today now.
"It was a massive performance by all the boys and I couldn't be more proud of them. Wales got one over us in the Six Nations (16-0 in Athlone) and it's our turn today."
Cian Kelleher darted over in the right corner late on for Ireland's bonus point score, with lovely hands in the build-up from Alex Wootton, Garry Ringrose and Ciaran Gaffney. It was chosen as one of the five best tries of round 2 - click here.
Related Links -
Ireland U-20s Slay Dragons In Titanic Celtic Clash
Video Highlights: Ireland Under-20s' Defeat To France
IRB Junior World Championship Fixtures/Results