The first big break of Tyshawn Taylor’s career, one might say, arrived at a playground in Clearwater, Fla., when Taylor was 8, shooting hoops alone outside his housing complex.

He had just moved from New Jersey and did not have a team or a coach or much instruction, but Stephanie Crawford, a local boys’ basketball coach, noticed him anyway. She encouraged him to sign him up for her A.A.U. team, Prime Time Hoops, spinning his career into motion. He went on to star at St. Anthony High School in Jersey City, N.J., and at the University of the Kansas. Then he was the 41st pick in last year’s N.B.A. draft — the first draft selection made by Brooklyn’s rebranded franchise (acquired via trade with Portland).

But it had been tough for Taylor, a 6-foot-3 pencil-thin point guard, to see the floor. He had been languishing on the bench and had already spent two stints in the Development League until, one might also say, his latest big break: the ankle injuries to Deron Williams last week.

With Williams out of the lineup Monday against the Indiana Pacers, Taylor stepped in and scored 12 points — including 7 in the fourth quarter and overtime — providing a sudden, unexpected glimpse at his N.B.A. potential. He made the most of his opportunity.