WASHINGTON — In a pair of unanimous decisions favoring law enforcement officials, the Supreme Court on Tuesday ruled for Arkansas police officers who had used deadly force to end a high-speed chase and for Secret Service agents who had moved protesters away from President George W. Bush.

The first case, Plumhoff v. Rickard, No. 12-1117, arose from a chase in 2004 that started in West Memphis, Ark., continued at high speeds on a highway and ended in a hail of 15 bullets in a parking lot in Memphis. The driver, Donald Rickard, and Kelly Allen, his passenger, were killed.

Whitne Rickard, the driver’s daughter, sued, saying the officers had used excessive force. The officers responded that they were entitled to qualified immunity, a doctrine that shields officials from suits over violations of constitutional rights that were not clearly established at the time of the episode.

The officers had acted lawfully and prudently, Justice Samuel A. Alito Jr. wrote for the court. (Justice Ruth Bader Ginsburg and Justice Stephen G. Breyer, though they voted with the majority, did not join all of Justice Alito’s analysis.)