Ryan Mee added 13 points in 23 minutes off the bench. Andy Larkin scored 12 points and had three assists.
Funso Lafe scored 20 for the Spartans. Carson Oren scored 19.
Rochester is 11-1 in the University Athletic Association, 22-1 overall. Case Reserve is 2-10 UAA, 4-19 overall.
Hauben sank three free throws and Larkin canned a 10 footer from right win in the last 2:05 of the first half to help Rochester take a 35-31 lead at halftime.
Case Western stayed close and led by four, 22-18, after Lafe drilled a three-pointer, then added a jumpshot with 8:57 left.
In the second half, the Spartans pulled within three on a trey by Matt Cannan, 46-43, with 13:06 to go. Hauben tipped in Larkin's miss, then Mee sank a three-pointer left of the key. It was 51-43.
Rochester sank 13 free throws in the final 3:43 to wrap up its 31st straight win at the Palestra.