Dublin made a decent start with points from Seán Gibbons (two), Nathan Nolan and Dylan Knight giving them a 0-4 to 0-1 lead.
Meath, however, battled back and Patrick Murtagh's goal put them in front by the 20th minute before Dublin closed out the half on top with points from Tom Keane and Ciarán Dowling to lead 0-7 to 1-3 at the half-time interval.
There was still just the minimum between the counties as the game entered it’s concluding 15 minutes.
Then Dublin struck for their crucial goal when sub Tiernan McGlynn found the Meath net and the Dubs added two further points to open up a six-point advantage.
The Royal County pressed hard over the closing few minutes but were denied a goal by a great James Cannon save. But the Royal County were rewarded with a late goal but Dublin held on to prevail by three points.
Afterwards Dublin’s influential centre-forward, Ciarán Dowling, was named the official Man of the Match.
Following their victories over Louth, Westmeath and Meath, the Coman Goggins-managed outfit progress to the Cup Final of the tournament where they will face Cavan in two Sundays time (July 27) in Oldcastle.
Dublin have won the tournament in the past two years but will face a Breffni County side who have outclassed Wicklow (7-13 to 5-8), Meath (7-12 to 1-9) and Monaghan (3-11 to 0-10).
T McGlynn 1-0, C Dowling, S Gibbons, T Keane 0-2 each, N Nolan, D Knight, J Rafter, C Hynes, B Redmond 0-1 each.
James Cannon (St Anne's); Ciarán Smith (Lucan Sarsfields), Rob Shaw (Castleknock), Conor Gibson (Nh Barróg); Aaron Carey (St Oliver Plunkett's/Eoghan Ruadh), Conor Ryan (St Vincent's), Seafra Fitzgerald (Na Fianna); Nathan Nolan (Kilmacud Crokes), Seán Gibbons (Castleknock); Tom Keane (Nh Olaf), Ciarán Dowling (Lucan Sarsfields), Jeff Rafter (Na Fianna); Tom Downes (O'Dwyer's), Dylan Knight (St Pat's, Donabate), Conor Hynes (St Peregrine's). Subs used: Eoghan Fitzpatrick (Ballinteer St John's), Aaron Duffy (Round Tower, Lusk), Bryn Redmond (St Sylvester's), Thomas Davis (Parnell's), Tiernan McGlynn (St Brigid's).