Tyrone lived on their wits in Navan before eventually shaking off dogged Meath after extra-time to advance to Round 2 of the All-Ireland football qualifiers.
Mickey Harte's side required a Cathal McShane point in the sixth minute of injury-time to force the extra period and Harry Loughran's 76th minute goal ultimately propelled them through.
But there was drama at the final whistle with Meath manager Andy McEntee held back from engaging referee Paddy Neilan after a controversial ending.
Meath, trailing by a point after scoring the last four points of extra-time, felt they deserved a free-in for a foul on James McEntee but Neilan waved play on.
The 2016 and 2017 Ulster champions can breathe a sigh of relief because they almost kicked themselves out of the Championship.
They hit 14 wides in normal time and racked up half a dozen goal chances that they didn't take, allowing Meath to almost pull of an upset win.
Ben Brennan had been terrific for Meath in the second-half of normal time with five points in that period and his last put Andy McEntee's men 0-14 to 1-10 ahead.
But they couldn't hold on as sub Ronan O'Neill played in Loughran for that crucial extra-time goal which settled a frantic affair.
Tyrone will be in Monday's draw for Round 2 of the qualifiers which take place on June 23/24 but Meath's season is over after a battling defeat to Ulster opposition for the second summer running.
Both counties came into the contest desperately seeking a win to ignite their summer after disappointing provincial exits.
Meath's loss in Longford was the bigger surprise though Tyrone were still left reeling by their defeat to Monaghan which ended their provincial three-in-a-row bid.
The Red Hands announced a late change before throw-in with Michael O'Neill replacing Niall Morgan in goals.
It didn't affect them as they dominated the first-half and cut Meath's defence asunder time after time to carve out gilt edged chances.
They scored just one goal in that half, a scrappy McAliskey effort in the eighth minute, but it could easily have been half a dozen.
McAliskey dragged another chance wide and hit the crossbar late in the half while Padraig McNulty drew a brilliant save from Meath 'keeper Andy Colgan.
McNulty also smacked an opportunity off the bar that wouldn't have counted due to a free in the buildup but it underlined Tyrone's supremacy.
The 2008 All-Ireland winners also blasted eight wides in the opening half and dropped a number of shots into Colgan's arms.
McAliskey was their principal attacking outlet and fired 1-05 of their 1-06 tally in the opening half.
Meath, in contrast, had five different scores though only racked up 0-07 in the half as they struggled to remain in the game.
The 2010 Leinster champions improved after the break and attacker Ben Brennan oozed quality.
He slotted back-to-back points to tie the game up at 0-09 to 1-06.
It set the tone for a thrilling second-half and the sides were level six times in an incident packed 40 minutes or so.
It was virtually score-for-score as Meath sharpened up in attack and Tyrone continued to be wasteful, booting six more wides.
Meath screamed for a penalty when O'Sullivan was hauled down in the 64th minute but ref Paddy Neilan only gave a free that Brennan converted.
Tiernan McCann was sent off two minutes later for Tyrone following an off the ball incident that left Brennan grounded.
And Brennan himself was dismissed for a second yellow card deep into injury-time.
He thought he'd just kicked the winner moments earlier but McShane popped up for Tyrone to send it to extra-time at 0-14 to 1-11.
With both teams back to 15, Tyrone dominated the opening half of extra-time and Loughran's palmed goal, after O'Neill's clever run and pass across the goal line, helped them to lead 2-14 to 0-15 at the break.
They didn't score again as Meath picked off four points in-a-row from O'Sullivan, Thomas O'Reilly, sub Shane Glynn and Donal Lenihan but they just couldn't reel in the northerners.
Tyrone: Michael O'Neill; Hugh Pat McGeary, Ronan McNamee, Padraig Hampsey; Tiernan McCann, Michael McKernan (0-01), Frank Burns (0-02); Colm Cavanagh, Padraig McNulty; Mattie Donnelly, Niall Sludden (0-01), Conor Meyler; Cathal McShane (0-02), Richard Donnelly, Connor McAliskey (1-08, 0-06f).
Subs: Kieran McGeary for Meyler (49), Rory Brennan for HP McGeary (49), Harry Loughran (1-00) for R Donnelly (53), Declan McClure for McNulty (62), Ronan McNabb for McNamee (68). Ronan O'Neill replaces red carded McCann for e/t, Meyler for McKernan (79), Conall McCann for McShane (86).
Meath: Andrew Colgan; Shane Gallagher, Conor McGill, Seamus Lavin; James McEntee (0-02), Sean Curran, Donal Keogan (0-01); Bryan Menton, Adam Flanagan; Mickey Burke (0-01), Ben Brennan (0-06, 0-03f), Cillian O'Sullivan (0-02); Graham Reilly, Donal Lenihan (0-04, 0-04f), Joey Wallace (0-01).
Subs: Thomas O'Reilly (0-01) for Lenihan (55), Eamon Wallace for Burke (56), Bryan McMahon for J Wallace (58). Cian O'Brien replaces red carded Brennan for e/t, Shane Glynn (0-01) for Gallagher (75), Daniel O'Neill for McGill h/t e/t, Lenihan for Lavin (84).
Referee: Paddy Neilan (Roscommon).