Born and raised in Western New York to German parents, Wurtenburg attended the prestigious Phillips Exeter Academy, where he played football.

He then accepted a coaching job at Dartmouth College, where for the next four years he led them to perfect records against both of their Triangular Football League opponents.

After ending his coaching career, Wurtenburg spent several years acting as a referee for Yale's football team.

[1] Wurtenburg began taking medical classes on his arrival at Yale, and joined the football team partway through his freshman year.

He was credited as one of the people who made the game "undoubtedly the finest ever played in America", according to writer Richard Melancthon Hurd.

Wurtenburg developed his own unique style at quarterback, regularly attempting "long, low, underhand passes" to his teammates to help set up scoring plays.

However, he was thrown out of the final game of the season, against Princeton, and Frank Barbour was given a guaranteed starting-quarterback slot for the rest of the time Wurtenburg was at Yale.

[19] In 1894, Wurtenburg was hired to replace former Yale teammate John A. Hartwell as the head coach of the US Naval Academy football team.

[22] Wurtenburg began his coaching career on October 6, leading his team to a 6–6 tie with the Elizabeth Athletic Club of New Jersey at Worden Field on the Naval Academy campus in Annapolis.

[26] Sometime during November, Wurtenburg returned from Germany along with fellow Yale medical graduate A.S. Cheney, and announced his intention to practice medicine in New Haven.

His team dropped two games to Yale and one to Army, but managed to defeat former Triangular Football League opponent MIT.

After that, Wurtenburg led his team to three straight victories, including wins over both Triangular Football League opponents.

[31][33] Wurtenburg retained his coaching position the next season, beginning the year with a blowout of Phillips Exeter, which was followed by three consecutive shutout losses.

Wurtenburg's team began the month with a shutout loss to Harvard, but recovered to win four straight games, defeating their conference opponents by a combined score of 74–12.

[37] After the conclusion of his coaching career, Wurtenburg opened up his first medical office, operating a short distance from his New Haven home.

[39] He was repeatedly selected by the university to act as an official in their home games; he was the school's referee in 1900 and 1901,[40][41] and returned to the position two years later, in 1903.

[47] He retained his membership with the Connecticut State Medical Society until at least 1920, maintaining his Elm Street office the entire time.

[A 1] The scholarship "is to be awarded to a member of the senior class who demonstrates character, leadership qualities, and promise of future usefulness".

Fred Crolius, captain of Wurtenburg's 1898 team, would later state that:[50] One man, whose influence more than any other one thing, succeeded in laying a foundation for Dartmouth's wonderful results, but whose name is seldom mentioned in that connection is Doctor Wurtenberg, who was brought up in the early Yale football school.