JJ Smith struck an equalising goal in the third minute of stoppage time as Carlow snatched a last gasp draw at O'Connor Park, Tullamore.
Carlow, who had two players red carded in the closing minutes, finished with a flourish to deny Meath victory.
The Royals also had Conor Gillespie dismissed during a fiery second half, but Smith's moment of opportunism means a replay will be required to see who advances to the Leinster SFC semi-final.
Initially it seemed as if Meath might pull clear especially when Cian Ward drilled a delightful 22nd minute goal to nudge them five ahead, but Carlow were plucky.
JJ Smith and Brian Murphy kicked Carlow's frees confidently and by the time the interval rolled around they had trimmed the deficit down to 1-6 to 0-7.
It had been particularly scrappy with Graham Reilly's dashing runs from deep the most impressive feature early on.
When Meath moved the ball quickly inside Brian Farrell, Joe Sheridan, and Ward carried a threat and they led by 0-5 to 0-3 by the 22nd minute.
Carlow corner back Padraig Murphy was outfoxed by Ward, who gathered a Sheridan delivery before grabbing a sweet goal.
But the underdogs responded outscoring Meath by four points to one in the lead up to the break so only two separated the teams at the turnaround.
After the restart there was plenty of drama as Carlow continued to battle admirably and Meath were disrupted. Graham Reilly extended Meath's advantage with a splendid effort, and while JJ Smith replied with two for Luke Dempsey's outfit Ward tapped one over for the Royals.
Then Meath midfielder Conor Gillespie was sent off in the 55th minute when picking up a second yellow card for dragging Brendan Murphy down.
In the next eight minutes six points were shared evenly as every team Carlow scored Meath instantly responded. That ensured that the favourites were 1-11 to 0-12 ahead with five minutes left on the clock, but then Meath landed a vital point.
Reilly, a constant menace, rifled a classy point from distance and then Paul Reid was sent off in the last minute for an off the ball incident. In stoppage time Carlow substitute Derek Hayden was also sent off for retaliating following a Sheridan foul, but Dempsey's side ploughed on defiantly.
Keith Jackson had a shot saved by David Gallagher and Smith poked home the rebound to force a replay, which will take place next Saturday evening in Tullamore.
Meath: D Gallagher; D Keogan, K Reilly, B Menton; D Tobin (0-1), S McAnarney, M Burke (0-1); C Gillespie, G Reilly (0-3); B Meade, P Gilsenan, A Forde; B Farrell (0-4), J Sheridan, C Ward (1-3, 2fs).
Subs: J Queeney for Forde (46 mins), M Collins for Gilsenan (53 mins)
Carlow: T O'Reilly; P Murphy, C Lawlor, B Kavanagh; K Nolan, S Redmond, T Bolger; Brendan Murphy (0-1), D Foley (0-1); Brian Murphy (0-3, 2fs), P Reid (0-1), E Ruth; JJ Smith (1-5, 4fs), S Gannon, D St Ledger (0-1, f). Subs: D Hayden for St Ledger (37 mins), B Lambe for Bolger (54 mins), K Jackson for Foley (62 mins), C Murphy for Brian Murphy (68 mins)
Referee: B Devlin (Derry).