A Gillian Joyce free - struck in the last minute of extra time - means Galway and Meath will have to replay their TG4 All-Ireland Ladies SFC quarter-final after a 3-11 to 1-17 draw this afternoon.
Meath moved ahead for the first time at O'Moore Park when Louise McKeever arrowed over a point with just six minutes remaining in extra-time, but substitute Joyce rescued a draw for the 2004 champions with her fourth point of the 80-minute duel.
The girls from the west had a stunning start, nabbing their three goals inside the first eight minutes.
They went 2-01 to 0-00 ahead - soccer international Niamh Fahey (penalty) and Geraldine Conneally both found the net following Anne Marie McDonagh's early point.
Fahey, who is in the Irish squad for next Saturday's Women's World Cup qualifier against Germany at Richmond Park, drew the foul for her third-minute spot kick, which she coolly dispatched to Irene Munnelly's right.
Fahey then turned provider, fisting through for the overlapping Conneally to slam past Munnelly. It got even better for PJ Fahy's side when Annette Clarke stole onto a Lorna Joyce pass and picked her spot for goal number three.
Meath, disappointing losers in both the National League and Leinster finals, looked out of it as they trailed by 3-04 to 0-05 at the interval. Three points from the boot of free-taker Jackie Shiels kept them in touch.
Thankfully the second half was much more evenly contested and the physically stronger Meath team's brand of possession football saw them claw back level by the 50th minute.
Substitute Michelle Doyle made an immediate impact, striking over twice, while statuesque wing-forward Grainne Nulty hit a purple patch with a quarter-hour remaining as she volleyed over three points in the space of four minutes. Team captain Mary Sheridan also claimed a number of vital high balls.
Katie O'Brien's 50th-minute goal drew the sides level at 3-07 to 1-13 and while Fahey won a second penalty, Munnelly foiled her this time with an excellent parry to her left.
Gillian Joyce and Shiels, who tallied up 0-07 by the finish, swapped late frees as the sides went into extra time on a 3-08 to 1-14 score line.
Galway were buoyed by the introduction of talismanic midfielder Lisa Cohill, who has been out with a cruciate injury for almost two seasons, and managed to push two points clear thanks to overs from McDonagh and Aoibheann Daly.
Spurred on by Sheridan, Meath dug deep and replied with three on the bounce - Shiels (0-02f) and McKeever both raised white flags.
Galway dominated the closing six minutes territorially, Cohill was thwarted by the post, but Joyce was on target after Clarke had drawn a close-in foul to ensure a second day out.
Galway: U Carroll; M O'Donnell, E Flaherty, M Glynn; C Cormican, A Daly (0-02), AM McDonagh (0-02); P Gleeson, C Molloy; E Concannon, A Clarke (1-00), N Duggan; G Conneally (1-01), N Fahey (1-01 (1-00 pen)), L Joyce (0-01).
Subs used: G Joyce (0-03 (0-02f)) for Glynn (21 mins), L Cohill for Gleeson (48), M Glynn for Clarke (56), H Carroll for Cormican (66 mins), P Gleeson for Duggan, A Clarke for Conneally (78 mins)
Meath: I Munnelly; S Dooley, E Lynch, S McCormack (0-01); J Rispin, L McKeever (0-01), C McAuley (0-01); J Burke, L Keenan (0-01); M Sheridan (0-01), J Shiels (0-07 (0-05f)), G Nulty (0-03); F Mahon, G Bennett, K O'Brien (1-00).
Subs used: M Doyle (0-02 (0-01f)) for G Bennett (34 mins), C O'Shaughnessy for Lynch (48), S Bennett for Keenan (70 mins), A Thompson for Rispin (80 mins).
Referee: Brendan Gallagher (Tyrone).