Jurors at Southwark Crown Court found her guilty of one count of misconduct. She will be sentenced later this month.
Britain's long-running phone-hacking scandal has led to dozens of arrests and to criminal charges against prominent journalists, including Prime Minister David Cameron's former communications chief. Other police officers and civil servants have also been questioned about possible wrongdoing.
The phone-hacking scandal has involved allegations of illegal snooping on celebrities, crime victims, politicians and others. Media mogul Murdoch closed the News of the World tabloid in July 2011 after many of its misdeeds were exposed. His media company has also paid out millions to numerous victims to avoid lengthy and expensive trials.
Tim Wood, the News of the World news editor who took Casburn's call, told the court that the detective expressed concern that counterterrorism resources were being diverted to the phone-hacking investigation. Wood also said Casburn complained of interference from Prescott, a prominent hacking victim and a vocal Murdoch critic.
"The one thing that stands out in my mind is the fact that she kept going on about Lord Prescott," Wood said. "Her saying that he was pressing for them to put charges on the News of the World, and she was saying that she felt it was wrong that he was interfering in the scandal, so to speak, and she resented that."
Casburn has been suspended with pay, the force said.
A News of the World reporter and a private investigator were jailed in 2007 for hacking into the voicemails of royal aides. But the newspaper denied there was a wider problem and the police investigation was closed.
Police reopened the investigation in early 2011 as new evidence emerged about the scale of the law-breaking.
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