A miraculous occurrence can be providential or heaven-sent, or just peculiarly fortunate and appropriate. In any event, as the word suggests, it has the character of a miracle.
The adjective miraculous has origins in the Latin word miraculum, meaning "object of wonder." It's often used to describe religious happenings, such as a direct answer to one's prayer. In a more secular context, a "miraculous comeback" is when a football team that's down by 30 points at halftime ends up winning the Super Bowl.