Does not happen in a major conference very often. Here are the records. Some of my western data is incomplete from earlier years so I might have missed a few:
Cornell, 1968; 38-29 = 9
Michigan State, 2001; 45-37 = 8
Michigan State, 1999; 47-40 = 7
Harvard, 1962; 36-30 = 6
Cornell, 1967; 37-32 = 5
Cornell, 1970; 42-39 = 3
Cornell, 2002; 36-34 = 2
Currently:
Cornell, 2003; 33-27 = 6
which means they could arguably become "the most effective defense of all time in conference play" with some really stifling D down the stretch.
Cornell, 2003: 39-29=10. Incredible.
And, as I mentioned on another thread...
Conference pts - OVERALL GA = 0!!!
for a team that only played 75.8% of games in conference.