Dublin suffered their first defeat in the Leinster football championship in 15 years.
The Meath side were able to hold on to their position and knock off the 14-time champions, finishing the match with a score of 0-23:1-16 in the semi-finals.
The Royals are set for a repeat of the 2010 final as they face Louth in the decider.
The Wee County side secured a place in a third successive final with a three-point win over Kielder.
Man of the match James Conlon bagged four points for Meath in the first half to secure a comfortable win.
Meath's Ciaran Caulfield and Dublin's Colm Busquell. Photo: Ryan Byrne/Inpho
He added another point after the break, while Eoghan Frain scored 14 points.
Speaking after the match, Conlon said: “We've been waiting for this moment for a long time.”
Meanwhile, Donegal face Armagh in the Ulster Football Championship final.
Jim McGuinness's side went into the decider with confidence, beating Down 1-19 to 0-16 in the semi-final.
Sourse: breakingnews.ie
