Wesley Saunders and Jonah Travis added 14 points apiece and Agunwa Okolie and Siyani Chambers had 10 apiece for the Crimson (12-5, 2-1 Ivy).
Steven Cook led the Tigers (8-10, 1-1) with 21 points. Amir Bell added 17 and Ben Hazel 15.
Bell scored the last nine points for Princeton, including two 3s in the final 13 seconds but it wasn't enough.
Saunders, whose two free throws at six seconds made it 75-69, also had eight assists, seven rebounds and three steals. Steve Moundou-Missi had 10 rebounds.
The Crimson led 39-29 at the half with Miller scoring 17 to match his career best.
Harvard made 20 of 29 from the line, 16 of 23 in the second half, while the Tigers finished 12 of 16.