fortuitous
A lucky accident or coincidence.
When something fortuitous happens, it occurs by chance in a way that turns out well. It's an unexpected piece of good luck: you didn't plan it, but you're glad it happened.
You might have a fortuitous encounter with exactly the person you needed to talk to, or make a fortuitous discovery when you stumble upon information that helps solve a problem. If you forget your lunch but your friend brings extra sandwiches, that's fortuitous timing. When a scientist accidentally leaves an experiment running overnight and discovers something important, that's a fortuitous mistake.
People sometimes confuse fortuitous with fortunate, and while they're related, they're not quite the same. Fortunate simply means lucky, whether you planned it or not. Fortuitous specifically emphasizes the accident or coincidence that led to the good outcome. Your grandmother giving you twenty dollars is fortunate. Finding twenty dollars on the ground is fortuitous.