O'Connor does not mention the moment of grace in the short story, but she talks about it in her letters. As she explains, the grandmother is an annoying woman, self-centered and self-righteous. By insisting on having her way and stopping by to see her old home (which turns out to be in another state), she is responsible for putting her family in harm's way and getting them killed by a psychopath called The Misfit, who happens by the family after their car rolls over. Throughout the story, the grandmother is always spouting off about her religious beliefs, but it is all words. She knows all the platitudes about "Jesus loves you", etc. -- in fact, she even tries to convince the Misfit to start praying.
The Misfit, however, is a psychopath who rejects God. He tells the grandmother he does not need to "pray to Jesus" because he is doing just fine by himself, which is not true. He is not doing fine at all. The grandmother, just before she dies, looks into his eyes and sees him as God sees mankind -- with love, even though mankind does not deserve God's love. When the grandmother realizes this, she reaches out to touch the Misfit, and it is then that he shoots her because he is evil and she has received God's grace, even at the moment of her death. By realizing that the Misfit is one of God's own children (the grandmother tells him, "Why, you are one of my babies. You're one of my own children") she is echoing the words of God, who created everyone and loves everyone, even though some (like the Misfit) reject his love. The grandmother does not reject God's love at the moment of her death, and that is her moment of grace.
Many of O'Connor's characters receive a "moment of grace" from God right before their death. You may be interested to know that in her letters, O'Connor referred to the grandmother as a heroine because she accepts God's grace.