Born and raised in Newark, New Jersey, Benkert received all-state honors at football while attending East Side High School in his hometown, before going on to play for the Rutgers University football team. With 16 touchdowns and four extra points for the 1924 Rutgers Queensmen football team, Benkert led the nation's college football players in scoring, with a total of 100 points; his 16 touchdowns also led the nation. His 1924 season included an October 4 game against Lebanon Valley College, won 56–0 by Rutgers, in which Benkert scored four touchdowns and kicked three extra points, scoring one of his touchdowns on an 86-yard run. Benkert gained a total of 2,124 rushing yards in his three collegiate seasons from 1922 to 1924, making him the first Rutgers player to cross the 2,000-yard mark.
After college, Benkert went professional, playing in the NFL for the New York Giants team that finished the season with an 8–4 record in its inaugural season in 1925, starting 10 of the team's 12 NFL games – typical of the less-regimented early barnstorming days in the league, the team played five games against non-league opponents -- and earning recognition as a first-team All-Pro by Collyer's Eye for his play that year. He played for the Pottsville Maroons in 1926, starting four games and appearing in eight as the team finished with a 10–2–2 record, good for third place in the league. In 1929 and 1930, Benkert played in New Jersey for the Tornados (the team moved from Orange to Newark in 1930), appearing in 13 games in his two seasons with the Tornados and also serving as a coach for a team that finished 3–5–4 in 1929 (in eighth place in the NFL among 12 teams) and 1–10–1 in 1930 (good for 11th, and last, place in the league). Characteristic of the experimental nature of the early National Football League, the Tornados experimented with using letters instead of numbers on player jerseys in the 1929 season; Benkert wore the letter "C" on his uniform in a game against the Frankford Yellow Jackets, while Johnny Tomaini had the letter "X" on his jersey.
After finishing his professional football career, Benkert went on to teach history and coach football at Orange High School in Orange, New Jersey, until his retirement from the school in 1971. He was a member of the football coaching staff at Rutgers in the 1940s.
List of NCAA major college football yearly scoring leaders
↑ 2.02.12.2Staff. "Heinie Benkert, 71, Played Halfback for Giants in 20's", The New York Times, July 17, 1972. Accessed January 17, 2018. "Henry (Heinie) Benkert, halfback in the 1920's for the New York Giants football team, died here yesterday. He was 71 years old. Mr. Benkert was a star in the early 1920's at Rutgers University, which he attended after winning all‐state honors in New Jersey on the Newark East Side High School team."
↑"Benkert, Rutgers Star, Holds Lead in Scoring Race", Reading Times, December 1, 1924. Accessed January 17, 2018. "He was unable, however, to overtake Heinie Benkert, and the Rutgers backfield marvel leads the final list with an even 100, the only player to reach the three-figure class."
↑Harvin, Al. "Rutgers Trounces Colgate", The New York Times, November 23, 1975. Accessed January 17, 2018. "The three 2,000 yard career men are Jennings, 2,934 (1971–73); Mitchell (2,286) ‘66–'68 and Heinie Benkert 2,124 from 1922 through 24."