Dublin manager Dessie Farrell said 'calm heads prevailed' as they withstood a Meath fightback to reach another Leinster final.
The All-Ireland champions led by 11 points at the interval and looked home and hosed, but a resurgent Meath hit an unanswered 1-04 after the restart to threaten a comeback.
A goal separated the teams with two minutes remaining but Dublin's big-match experience came to the fore late on, holding onto possession for long spells to tire an already wilting Meath and kick three injury-time points.
"It was the proverbial game of two halves," Farrell told RTÉ Sport. "We were very good in first half and not so good in the second.
"We made it a contest and to be fair to Meath, they threw everything at it in the second half, which we knew they would. We were expecting it so it was no surprise. We found it difficult to deal with though.
"The game was in the melting pot for longer than we would have liked. It was good to see the bit of composure come back into our play at the end. We finished quite strongly in the last couple of minutes."
A Cormac Costello penalty separated the teams at the first water break but Dublin then shifted up a gear, hitting 1-06 without reply with a Con O’Callaghan piledriver rattling the net.
Dublin led by 2-11 to 0-06 at the interval and seemed on course for another landslide Leinster Championship win, but Mathew Costello’s goal kickstarted a Meath revival as the Dubs lost their way in front of goal.
"First half there was a lot to be happy about, many pleasing aspects, but it was the exact opposite in the second half for long periods," said Farrell, whose side scored two points in 35 second-half minutes before rediscovering their scoring touch in added time.
"There’s a lot of experience in that team. They’ve been in those tight situations before and managed that period well.
"Obviously we need to take a look at how we ended up in that situation in the first instance, and we’ll do that, but definitely calm heads prevailed late in the game."
Farrell’s counterpart Andy McEntee praised his players’ fighting spirit as Meath mounted an unlikely comeback.
"We gave it everything we had for the second half," said McEntee. "The first half wasn’t what was required and what we expected. Second half we certainly gave it a good shot."
Meath had a first-half penalty claim turned down by referee Conor Lane and moments later the Cork official pointed to the spot at the other end after Séamus Lavin and Costello were adjudged to have fouled Brian Fenton as he charged towards goal.
"It's very hard to see but it certainly looked like we had a legitimate claim," said McEntee.
"I got the impression the one at the far end, the fella was watching too much soccer at the Euros."