Gogolak attended and played college football at Cornell University, where he was elected to the Sphinx Head Society and was a member of Delta Upsilon fraternity.  Gogolak, reflecting his roots in European soccer, instead approached the ball at an angle and kicked it with his instep. Upon graduation in 1964, he was signed by the American Football League's Buffalo Bills, bringing yet another innovation to the upstart league that had become known for its experimentation: the unorthodox style that had made Gogolak notable while in college now made him professional football's first "soccer style" (as opposed to "conventional") kicker. In 1965, he scored 115 points and was selected by his peers as a Sporting News AFL All-League player.
Gogolak was also a prime factor in the "war between the leagues" and the subsequent merger of the National Football League with the American Football League. Bills owner Ralph C. Wilson, Jr. paid Gogolak $10,000 in 1964 and offered him $13,500 for 1965, exceptional pay, in those days, for a kicker. Choosing instead to take a reduction in pay to $9,900, Gogolak, like a later restricted free agent, was able to "play out his option," thereby forcing the Bills to match any other team's subsequent offer. Fortunately for Gogolak, a wealthy suitor was at hand. The NFL's New York Giants, playing in the NFL's largest market, found itself saddled with struggling rookie kicker Bob Timberlake. The Giants, having witnessed Timberlake miss his thirteenth consecutive kick, ignored the owners' "gentleman's agreement" against signing another league's players, an arrangement that had previously depressed player wages and prevented inter-league competition over otherwise valued athletes. The desperate Giants, then playing in a Yankee Stadium whose mid-winter winds sometimes rivaled those faced by Gogolak in Buffalo, signed the Bills star; Gogolak would go on to become the Giants' all-time leading scorer. As NFL owners had feared, the signing led to a marked increase in similar "poachings" by AFL Commissioner Al Davis, bringing other NFL stars to the newer league. Ultimately, this increasingly expensive competition for key players was a significant contributory factor to the two leagues' owners reaching accord in the AFL-NFL Merger.