In late January, the Compton, Calif., rapper Kendrick Lamar lost the Grammy Award for album of the year to Bruno Mars. “DAMN.,” Mr. Lamar’s fourth LP, was his third straight to be nominated but ultimately fall short of the trophy, considered by most to be the top prize in popular music.

But perhaps not anymore.

On Monday, Mr. Lamar’s “DAMN.” took home an even more elusive honor, one that may never have even seemed within reach: the Pulitzer Prize for music. Mr. Lamar is not only the first rapper to win the award since the Pulitzers expanded to music in 1943, but he is also the first winner who is not a classical or jazz musician.

“The time was right,” Dana Canedy, the administrator of the prizes, said in an interview after the winners were announced. “We are very proud of this selection. It means that the jury and the board judging system worked as it’s supposed to — the best work was awarded a Pulitzer Prize.”