I believe that the title most accurately reflects the main idea of the story, which is the fact that Johnsy, the main focus of the story, who was desperately ill and close to death was inspired to live by, what she believed, was the last leaf on an old vine.
She had given up all hope of living and the last leaf's stubborn persistence became a symbolic image for her own survival. If the fragile leaf could endure whatever nature threw at it, she would be able to do so as well. When she saw that the leaf was clinging to life, she decided to do the same and that is what saved her.
It does not matter that the leaf was not real, for she did not know that. Johnsy had been counting the leaves on the ivy, noticing that they were all disappearing fast. She told Sue:
"...When the last one falls I must go, too. I've known that for three days. Didn't the doctor tell you?"
The fate of the last leaf, therefore, became inseparably intertwined with hers. She emphatically believed that if it went, she had to go too, as she tells Sue:
"...I want to see the last one fall before it gets dark. Then I'll go, too."
When the leaf refused to fall, she decided to fight just as hard to survive as it did, as she tells Susie:
"Something has made that last leaf stay there to show me how wicked I was. It is a sin to want to die..."
The situation is dramatically ironic since the leaf was no leaf at all but a masterful painting of one. The artist, Old Behrman, cared so much for Johnsy that he went out into the storm and painted the leaf against the wall, once the real one had actually fluttered off. This, in effect, became his triumphant masterpiece. His work of art saved another's life.
However, this act of kindness came at a great price, for the frail old man contracted pneumonia for being out in the terribly cold and wet weather and died soon after. This, in itself, makes the title even more fitting because Old Behrman's last painting of a 'last leaf' had been his greatest and best.