Resta was born in Faenza, Italy, and moved to England with his family at the age of two. He began racing at Brooklands in 1907 when he took part in the inaugural Montagu Cup, the very first race staged at that new circuit. He later set a record of 95.7 mph in a half-mile run at Brooklands. On 2 October 1913, alternating in two-hour spells with Jean Chassagne and Kenelm Lee Guinness, Resta set a series of long-distance world records driving a single-seater Sunbeam Grand Prix car. He also competed in European Grands Prix, including the 1913 French Grand Prix, before turning his attention to the United States.
Resta arrived in the United States in early 1915, brought over by Alphonse Kaufman, an American importer of Peugeots, to drive a Peugeot EX3. Shortly after arriving he married Mary Wishart, sister of racer Spencer Wishart, who had died the previous year.
In February 1915 he won the United States Grand Prize at San Francisco, then followed it with victory in the Vanderbilt Cup. He came agonisingly close at that year's Indianapolis 500, leading in the final stages before skidding and pitting for tyres, ultimately finishing second to Ralph DePalma. He rounded out the season by winning the inaugural 500-mile race at the Chicago Speedway on 26 June 1915.
The 1916 season was Resta's finest. En route to the American National Driving Championship, he won the Vanderbilt Cup for the second consecutive year and claimed victory at the Indianapolis 500, along with victories at the Chicago 300, the Minneapolis 150, and the Omaha 150. With the United States entering World War I in 1917, racing was sharply curtailed, and Resta's opportunities diminished.
In 1923, at the age of 39, Resta returned to competition. He made appearances at Beverly Hills and attempted Indianapolis again, retiring after 225 miles. Competing in Europe, he finished third in the Penya Rhin Grand Prix and won the voiturette class at the Spanish Grand Prix. He joined the Sunbeam factory team for 1924, alongside Henry Segrave and Kenelm Lee Guinness.
Resta was killed on 3 September 1924 at Brooklands while attempting a new land speed record in a Sunbeam. A belt broke on the second lap, puncturing a tyre and sending the car out of control; it crashed through a corrugated iron fence on the Railway Straight and caught fire. His riding-mechanic Bill Perkins was hospitalised in the accident, an incident that also indirectly led to a serious crash for Guinness at the San Sebastian Grand Prix when a substitute mechanic, Tom Barrett, was killed — contributing to the abolition of riding-mechanics in Grand Prix racing.
Resta was inducted into the Auto Racing Hall of Fame in 1954. His twin Vanderbilt Cup victories and his 1916 Indianapolis 500 win mark him as one of the most accomplished racing drivers of the pre-war American scene, a pioneer who bridged the European Grand Prix world and the American board-track and speedway circuits of the 1910s.