Palace twice hauled themselves back from the brink on a pulsating afternoon in South London. A quickfire Jean-Philippe Mateta double brought them level midway through the second-half, after the Eagles had trailed 2-0 at the break.
But Bournemouth struck in the dying minutes of normal time through Ryan Christie to re-take the lead. At that point Glasner's side were staring at a first home league defeat of the season.
Yet in the 97th minute Marc Guehi was wrestled to the ground by Bournemouth's Bafode Diakite as a left-wing corner was taken.
That gave Mateta a chance from the penalty spot, which he duly converted. Roared on by the Palace faithful, there was even still time for the Palace forward to miss a late chance to win it.
Glasner was willing to hold his hands up after the thrilling contest, admitting that he didn't expect quite so much goalmouth action before the game.
"It looks like I don't know what I'm talking about," joked Glasner. "Even managers can be wrong. I was convinced that this would be a completely different game, but they were so efficient today, they had eight shots and scored three goals.