Kearns won one of the best known patent infringement cases against Ford Motor Company (1978–1990) and a case against Chrysler Corporation (1982–1992). Having invented and patented the intermittent windshield wiper mechanism, which was useful in light rain or mist, he tried to interest the "Big Three" auto makers in licensing the technology. They all rejected his proposal, yet began to install intermittent wipers in their cars, beginning in 1969.

Kearns was born in Gary, Indiana. He grew up near the large Ford plant in River Rouge, Michigan, a city south of Detroit. His father worked for the Great Lakes Steel Corporation.

He excelled in cross-country foot racing during high school, was a talented violinist, and became a teenage intelligence officer when he served in the armed services. Kearns was a member of the Office of Strategic Services, the forerunner of the U.S. CIA, during World War II.

He earned engineering degrees from the University of Detroit and Wayne State University and a doctorate from Case Western Reserve University.

It is reported that the inspiration for his invention stems from an incident on Kearns' wedding night in 1953, when an errant champagne cork shot into his left eye, which eventually went almost completely blind. Nearly a decade later, in 1963, Kearns was driving his Ford Galaxie through a light rain, and the constant movement of the wiper blades irritated his already troubled vision. He modeled his mechanism on the human eye, which blinks every few seconds, rather than continuously. Kearns later downplayed his courtroom story of the inspiration and played up a more conscious, deliberate inventive process.

He sued Ford Motor Company in 1978 and Chrysler Corporation in 1982 for patent infringement. The Ford case went to trial in 1990, and there were two trials. Ford lost, although the court held that Ford's infringement was not willful (meaning that damages for infringement would not be enhanced). Ford agreed to settle with Kearns for US$ 10.1 million with an agreement of no further appeals.

After the settlement with Ford, Kearns mostly acted as his own attorney in the subsequent suit against Chrysler, even questioning witnesses on the stand. The Chrysler verdict was decided in 1992, and was a victory for Kearns. Chrysler was ordered to pay Kearns US$ 18.7 million with interest. Chrysler appealed the court decision, but the Federal Circuit let the judgment stand. The Supreme Court declined to hear the case. By 1995, after spending over US$ 10 million in legal fees, Kearns received approximately US$ 30 million in compensation for Chrysler's patent infringement.

Chrysler was represented by Harness Dickey and Pierce, one of the first firms Kearns went to when he contemplated suing Ford in the late 1970s. Indeed, according to his son Dennis Kearns, Kearns wanted Harness Dickey removed for conflict of interest, but was unable to convince his attorneys to make a motion to remove Harness Dickey. He then decided to manage the Chrysler litigation on his own with his family. However, this strategy did not seem to work out well in subsequent litigation against GM, Mercedes, and Japanese companies as he missed deadlines for filing papers and his cases were dismissed.

In the late 1990s, he served on the board of directors of the Veterans of the Office of Strategic Services and the General William J. Donovan Memorial Fund.

On February 9, 2005, Kearns died of brain cancer complicated by Alzheimer's disease in Baltimore, Maryland. The story of his invention and the lawsuit against Ford forms the basis of the 2008 film, Flash of Genius. Robert Kearns and his wife Phyllis were divorced. According to the movie, Phyllis left Robert due to the stress of the court and decided to live on her own. They had two daughters, four sons, and, at the time of his death, seven grandchildren.