At Loyola, he served as captain of the team that made a run through the 1963 NCAA Tournament to win the national championship. In the first round of the tournament, Loyola defeated Tennessee Tech by 111–42, which remains the largest margin of victory (69 points) in an NCAA Tournament game. In the second round, Loyola faced Mississippi State in a historic match now known as the Game of Change. Facing Loyola's lineup with four black starters, Mississippi State defied segregationists by participating, breaking an unwritten law against Mississippi teams competing against teams with black players. Harkness was enshrined in history as he shook hands Joe Dan Gold, the white captain of Mississippi State, prior to tip-off. In a 2013 interview, Harkness told NPR of the handshake: "The flashbulbs just went off unbelievably, and at that time, boy, I knew that this was more than just a game. This was history being made." Loyola beat Mississippi State, then sailed past Illinois and Duke to reach the tournament final. Loyola then upset the Cincinnati Bearcats in overtime to win the 1963 NCAA Basketball Championship. Harkness and the other four Loyola starters played the entire game, without substitution.