The lowest final score of a college basketball game was 12 to 10. The game was between Duke and N.C. State in an ACC Tournament game in 1968.
Prior to the advent of the shot clock teams were able to dribble for long periods of time without penalty. At one point a player dribbled continuously for over 13 minutes without shooting or passing.
The lowest scoring game since the inception of the shot clock, referred to as the "shot clock era," was in 2005 when the Monmouth University Hawks beat the Princeton Tigers 41 to 21.