It took nearly three weeks, 12 closely fought games and a day of high-speed tiebreakers to decide the World Chess Championship, but at the end of play on Wednesday, victory went to Magnus Carlsen, the Norwegian grandmaster, leaving Sergey Karjakin to return home to Russia in noble defeat.

“Karjakin only wanted to prove he was Carlsen’s equal,” said Denes Boros, a Hungarian grandmaster and chess commentator who was at the event. “Carlsen came to prove he was greater.” In the end, he was.

Wednesday was Mr. Carlsen’s 26th birthday, which he said earlier in the week had been good luck in the past. Mr. Karjakin is also 26, making them the youngest pair ever to face off in the world championship.

Spectators at the Fulton Market Building in Lower Manhattan, many of them students of past championships, declared the match outstanding, with each player pressing minute advantages or finding inventive defenses against whatever attack the other threw at him.