Con O'Callaghan kicked 1-7 of a 1-12 to 0-9 victory over Meath at Parnell Park, to set up a semi final meeting with either Laois or Wicklow.
Westmeath will face Kildare in the other semi.
Kildare comfortably saw off Offaly at Hawkfield, while Westmeath edged out Wexford by a solitary point in Enniscorthy.
