Born in Biccari in the Apulia region of southern Italy, DePalma emigrated with his family to the United States in 1891. Questions about his citizenship were not resolved until 1920, when it was established that his father had not completed naturalisation paperwork; DePalma formally applied for and received US citizenship in August of that year. As a young man he tried bicycle racing before turning to motorcycles, then made the transition to automobile dirt track racing in 1909, the year the American Automobile Association established the national driving championship.
DePalma achieved immediate success in car racing. In 1911 he won the first Milwaukee Mile Championship Car race. He captured the American AAA national dirt track championship in 1908, 1909, 1910, and 1911. By 1934, after 27 years of racing, he estimated his career earnings at $1.5 million.
His most famous early moment was not a victory but a defeat. At the 1912 Indianapolis 500 DePalma led for 196 of the race's 200 laps — taking the lead on lap 3 and maintaining it through almost the entire race — before a cracked piston stopped his 1910 Mercedes with just two laps remaining. He and his riding mechanic pushed the car across the finish line, completing only the 199th lap and taking eleventh place without any prize money. The Mercedes from that race is preserved in the Indianapolis Motor Speedway Hall of Fame Museum.
DePalma won the Elgin Trophy at Elgin, Illinois in 1912 and again in 1914, and captured his greatest single-race triumph in 1914 when he defeated the faster car of Barney Oldfield to win the Vanderbilt Cup on the roads of Santa Monica, California. Driving a Mercedes known as the "Gray Ghost," he employed tactical mastery to overcome a horsepower deficit — a victory he rated the best of his career. That year he also clinched his second US national driving championship.
In 1915 he drove a Mercedes Grand Prix car — the same model that had dominated the 1914 French Grand Prix in a 1-2-3 result — to victory at the Indianapolis 500, his crowning achievement on the oval. His total of 612 laps led at Indianapolis stood as the all-time record there until Al Unser surpassed it on the 200th lap of the 1987 Indianapolis 500.
DePalma also competed internationally. On 12 February 1919 he drove a Packard to a world speed record of 149.875 mph over a measured mile at Daytona Beach, Florida. In 1920 he drove for Ballot at Indianapolis, setting pole position but retiring with bearing failure. The following year he travelled to Le Mans for the 1921 French Grand Prix, finishing second behind Jimmy Murphy's Duesenberg. He won the Canadian national championship in 1929 and continued racing in stock cars until retiring in 1936.
DePalma was known for exceptional sportsmanship, making him widely popular with fellow drivers and spectators alike. His career was threaded with dramatic reversals: the 1912 Indianapolis push across the line became one of the sport's enduring images of determination and misfortune. Despite such setbacks, his record — four national championships, 25 Championship car wins, and a speed record — places him among the most accomplished American racing drivers of the pre-war era.
In 1923 DePalma established the DePalma Manufacturing Company in Detroit to build race cars and aircraft engines. He served as an honorary referee at the Indianapolis 500 on multiple occasions, his final appearance in 1954. He died on 31 March 1956 in South Pasadena, California, from cancer, and was interred at Holy Cross Cemetery in Culver City. He was inducted posthumously into the Automotive Hall of Fame in 1973 and into the International Motorsports Hall of Fame in 1991.
He is also the maternal uncle of 1925 Indianapolis 500 winner Peter DePaolo.