The Royals had been written off following their heavy Leinster final defeat by Dublin, while Tyrone went into the game on a high following an impressive Ulster championship campaign.
And in a thrilling tie which was level on six occasions, the Red Hands were on the cusp of victory when Meath struck gold right at the death.
Meath made a dream start with a goal after 12 seconds, Barry Dardis palming to the net after Jason Daly and Cillian O’Sullivan had combined on the right. Tyrone responded with a superb fifth minute goal, Sean Hackett slicing through the Royal defence to drill the ball to the net to set the scene for a terrific first-half.
Meath got on top at midfield, Adam Flanagan and Shane McEntee giving them a vital edge, and a string of Meath points, Stephen Coogan hitting some gems and O’Sullivan also on target, saw them open out a three-point lead.
Tyrone lifted the siege, the hard-working Ruairi Sludden and Michael Cassidy engineering a revival, and Danny McNulty thumped over a long-range point, before Mark Bradley’s fourth had them back in front. But the sides went in at the break on level terms after Coogan nailed his fourth to tie it up at 1-7 each. Fiachra Ward stepped up to the mark with two long range frees early in the second-half and Meath has just gone back in front through Ward when the Red Hands crafted a goal chance, Bradley sending Hackett away, but his effort was superbly saved by sub goalkeeper Robert Burlingham.
Tyrone missed a handful of opportunities, but clawed back points through Michael Cassidy and James McGahan.
McGahan’s second score had the Red Hands just a point behind going into the final 10 minutes, but McEntee and Flanagan raised their game again and Ward stroked over another free.
Tyrone midfielder Anthony Devlin won some vital ball for Bradley to angle over a couple of superb points to tie it up at 1-12 each and set up a thrilling climax. But Meath rallied for O’Sullivan to cross from the right, and when the Tyrone defence failed to clear, Coogan scrambled over a dramatic winning goal.
Tyrone finished with 14 men, defender Conor Mallon receiving a straight red.
Scorers for Tyrone: S Hackett 1-2 (0-1f), M Bradley 0-6, J McGahan 0-4 (2fs), M Cassidy, D McNulty 0-1 each.
Scorers for Meath: S Coogan 1-4, B Dardis 1-0, F Ward 0-4 (3fs), C O’Sullivan 0-3, J Daly 0-1.
TYRONE: D Martin, R Mullan, P Hampsey, C Harvey, C Corr, C Mallon, R Brennan, D McNulty, A Devlin, K McGeary, M Cassidy, R Sludden, M Bradley, J McGahan, S Hackett.
Subs: R McGlone for Sludden, D Carroll for McNulty.
MEATH: J Hannigan, D Smith, B Power, S Gallagher, P Kennelly, P Harnan, R O Coilean, A Flanagan, S McEntee, C O’Sullivan, J Daly, J McEntee, B Dardis, S Coogan, F Ward.
Subs: R Burlingham for Hannigan, A Neary for Smyth, P Kennelly for Daly.
Referee: F Kelly (Longford).