Meath moved ahead for the first time when Louise McKeever arrowed over a point with only six minutes remaining in stoppage time, but substitute Joyce rescued a draw for the 2004 champions with her fourth point of an enthralling duel.
The girls from the west had a stunning start, nabbing their three goals inside the first eight minutes. They went 2-1 to no score ahead after 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 home. It got even better for PJ Fahy’s side when Annette Clarke stole on to a Lorna Joyce pass and picked her spot for goal number three.
Meath, losers in both the National League and Leinster finals, looked out of it as they trailed by 3-4 to 0-5 at the interval. Only three points from the boot of free-taker Jackie Shiels kept them in touch.
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Thankfully, the second half was more evenly contested and the physically stronger Meath’s brand of possession football saw them claw level by the 50th minute.
Substitute Michelle Doyle made an immediate impact, striking over twice, while wing forward Grainne Nulty hit a purple patch with a quarter-hour remaining, volleying over three points in four minutes. Captain Mary Sheridan contributed by claiming a number of vital high balls.
Katie O’Brien’s 50th-minute goal drew the sides level at 3-7 to 1-13. Fahey then won a second penalty, but Munnelly foiled her this time with an excellent parry to her left.
Joyce and Shiels, who tallied 0-7 by the finish, swapped late frees as the sides went into stoppage time with a 3-8 to 1-14 scoreline.
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.
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Spurred on by Sheridan, Meath dug deep and replied with three on the bounce, Shiels (2f) and McKeever raising the white flags.
Galway dominated the closing six minutes territorially. Cohill was thwarted with by the post but Joyce was on target, after Clarke had drawn a close-in foul, to set up a replay.