UUJ set up a Sigerson Cup semi-final against DCU as they edged out competition hosts NUI Galway 0-12 to 1-6 at Dangan on Wednesday.
The sides were level at 0-6 to 1-3 at half-time in Galway but Adrian McGuckin's side pulled clear in the second half.
DCU eased past another Dublin outfit 1-15 to 0-7 on Wednesday while UCC edged out Sligo IT 2-7 to 0-11.
The remaining quarter-final sees UCD facing Maynooth on Thursday evening.
Maynooth, who beat Queen's in the first round, will have home advantage for the last eight game.
Jordanstown, the only remaining Ulster team left in the competition, now go forward to the finals weekend on 24/25 February in Galway.
Queen's University Belfast and St Mary's College lost their first-round ties two weeks ago.
Irish Daily Mail Sigerson Cup quarter-finals
UCC 2-7 0-11 Sligo IT
UUJ 0-12 1-6 NUI Galway
DCU 1-15 0-7 DIT
NUI Maynooth v UCD (Thursday 1900 GMT at Maynooth)