Faulkner was born in Tell, Childress County, Texas. His family relocated frequently — to Milledgeville, Georgia, when he was two-and-a-half, then to Lake Wales, Florida, and eventually to San Diego, California, in 1936. Standing 5 feet 4 inches and weighing 130 pounds, he earned the nickname "The Little Dynamo" for his aggressive driving style.
Faulkner began racing motorcycles in 1936 shortly after settling on the West Coast. By 1938 he had switched to automobiles, making his car-racing debut at a midget event in Bakersfield, California. He drove for the Edelbrock dirt track racing team and rapidly became one of the leading midget car racers on the Pacific Coast, capturing the United Midget Association Pacific Coast championship in 1941 with 32 feature wins that season. World War II halted organized racing from 1942 to 1945. When competition resumed he continued to accumulate victories; his postwar tally on the URA circuit reached 41 feature wins through 1949. A second-place finish in the Turkey Night Midget Grand Prix at Gilmore Stadium in 1948 was among his notable results in that period. He was later inducted into the National Midget Auto Racing Hall of Fame in 2007.
Faulkner made his first attempt at AAA National Championship events in 1949 but did not qualify for the Indianapolis 500 or secure a championship start that year. His breakthrough came in 1950. Driving the Agajanian Special — a Kurtis Kraft 2000 chassis powered by an Offenhauser engine, entered by J.C. Agajanian — he qualified on pole for the Indianapolis 500 on May 13, becoming the first rookie to achieve that distinction. His four-lap average of 134.343 mph shattered existing records; one individual lap of 136.013 mph was the fastest of the day. On race day Faulkner ran to seventh place after 135 laps. He went on to win the Milwaukee 200 that season and finished second in the AAA National Championship standings with 1,317 points, just behind champion Henry Banks.
In 1951 Faulkner elevated his performance further. He won the Darlington 250 — starting from deep in the field — and repeated at the Milwaukee 200, taking his third career AAA victory. He finished third in the points standings with 1,513.6 points across nine starts, with multiple additional podiums that year. After 1951 his Championship Car activity became more sporadic. He returned for the 1955 season driving the Merz Engineering Kurtis Kraft 500C for the Indianapolis 500, qualified seventh at 139.762 mph, and finished fifth after completing all 200 laps — his best Indianapolis result.
Faulkner started four Indianapolis 500s between 1950 and 1955. In 1951 he retired after 123 laps with crankshaft failure. He failed to qualify in 1952. In 1953, entered by Eugene Casaroll in a Kurtis Kraft 500A, he ran all 176 counted laps to finish 17th. The 1955 run was a shared drive with Bill Homeier, each driver receiving one championship point. He did not qualify for 1954. His pole in 1950 briefly made him the youngest Formula One World Championship polesitter, at 30 years and 103 days.
The Indianapolis 500 counted toward the FIA Formula One World Championship from 1950 to 1960. Faulkner's four starts at Indianapolis during those years gave him six total Championship entries (five starts). He accumulated one career World Championship point, from his shared fifth-place in 1955. His 1950 pole was the fastest qualifying lap in the young championship's history at that point.
From 1952 to 1954 Faulkner drove in the Carrera Panamericana, a grueling road race across Mexico that held World Sportscar Championship status. He competed as a works driver for the Lincoln Capri team managed by Bill Stroppe and Clay Smith. In 1952 he recorded two second-place class finishes. In 1953, co-driving with Chuck Daigh, he placed ninth overall. In 1954, partnered with Francis W. Hainley, he finished tenth overall.
On the night of April 21, 1956, Faulkner competed in a race at Gardena Speedway near Los Angeles and then drove nearly 500 miles overnight to reach Vallejo, north of San Francisco, where a USAC Late Model Championship qualifying session was scheduled the following day. On his first qualifying lap at the 5/8-mile dirt West Coast Speedway, his #22 1956 Ford owned by J.C. Agajanian struck a rut in turn 3. The car skidded sideways and flipped five times. Faulkner's seat belt stretched and he was partially ejected; the car rolled on top of him. He was taken to a hospital in Vallejo and died approximately one hour after arrival. He was the first fatality in USAC Late Model Championship history.
Shortly after the accident, George Amick went out on the same circuit in another 1956 Ford and struck the same rut. Amick's car also flipped repeatedly, though he survived with a broken wrist. Faulkner's crash prompted wide discussion about the reliability of seat belts — then relatively new equipment — and raised questions about whether fatigue from the overnight drive may have contributed to the accident.
Faulkner was survived by his wife Mary and daughters Linda and Patricia Ann. In his later years he had operated a lawn mower business in Long Beach, California. He was inducted into the West Coast Stock Car Hall of Fame in 2006.