“Everything I was working for and dreaming came today,” said Cilic, a 25-year-old Croat who can now shave his lucky beard if he chooses. “And I feel for all those other players who are working hard this is a big sign and big hope that if you are working hard things are going to pay off.”

Such signs have been scarce in this tennis era dominated by so few men. A year ago, Cilic, a semifinalist at the 2010 Australian Open, was unable to play here at all. He missed the tournament because he was serving a suspension after testing positive for a banned stimulant. Though he faced a possible two-year ban, he appealed, arguing that he had unintentionally ingested the substance in a glucose tablet, and succeeded in having the suspension reduced to four months.

“It angered me how all the process went, because it was not fair to me,” Cilic said last week. “It wouldn’t be fair to any tennis player. So that was just very bad memories.”

But against a big organization, he said, “you can’t do much. So I just accepted it. When I came back to tennis court, I erased it from my memory. I just used the positive parts, which, you know, made me tougher.”

He returned to the tour in October and rose in the rankings. He arrived in New York seeded 14th and with two titles already to his credit in 2014. But it would have taken quite a soothsayer to predict that from that platform, he would claim the Open trophy at a time when outsiders have so rarely managed to reach the finish line at major tournaments.