WASHINGTON — Doug Evans, a white prosecutor in Mississippi, has spent decades trying to convict Curtis Flowers, a black man, of the 1996 murders of four people inside a furniture store. Over the course of six trials, Mr. Evans relied on a signature tactic: he worked diligently to keep black people off Mr. Flowers’s juries.

The sixth time, Mr. Flowers was convicted and sentenced to death. But he appealed and eventually the case reached the Supreme Court in a case that attracted a great deal of attention, including being featured on a season-long podcast as well as in episodes of a documentary series.

In a lopsided decision, the Supreme Court ruled on Friday that Mr. Evans had violated the Constitution. Only two of the court’s most conservative members — Justices Clarence Thomas and Neil M. Gorsuch — dissented. And writing the majority decision was another of the court’s conservatives, its newest — Justice Brett M. Kavanaugh, in perhaps his most significant role on the court since he joined it last fall after an unusually bitter confirmation battle which included the fervent opposition of Democrats.

As is customary, Chief Justice John G. Roberts Jr. gave no reason for assigning the majority opinion to Justice Kavanaugh. But the high-profile assignment may have been prompted by Justice Kavanaugh’s longstanding interest in the issue. When he was a law student at Yale, Justice Kavanaugh wrote an article in The Yale Law Journal calling for vigorous enforcement of a 1986 Supreme Court decision barring race discrimination in jury selection.