Meath proved too strong for Offaly who despite scoring two goals were ultimately dismissed comfortably by 2-07 1-20 in Portlaoise on Sunday.
The result means the Royals will go onto the Leinster SFC quarter-final against Laois on 13 June.
Cian Ward was in fine form, kicking eight points during the game for his county and helped bring his side into the break leading by 0-11 to 2-03.
However, Meath didn’t have it all their own way with Brian Connor and Ken Casey getting a goal each for Offaly.
Resistance finally began to crumble when Offaly midfielder John Coughlan was given a straight red card on 39 minutes and Meath were in the driving seat for the rest of the game.
Joe Sheridan put the final nail into Offaly’s coffin when he pounced late on and got a deserved goal from close range.
Both players and referee struggled with the new hand-pass rule changes and the play was held up on a number of occasions for debatable infractions.
