Laurent Rivard added 12 points, Siyani Chambers 11 and Wesley Saunders 10 for Harvard (15-7, 7-1), which has won two straight and six of seven. Christian Webster, who scored eight points with five rebounds and four assists, became Harvard's winningest player, picking up his 85th career victory.
Smith, who was 5 of 5 from the field and 4 of 4 from the line, also had seven rebounds and six blocks.
Trailing 26-24, Harvard closed out the first half on an 8-2 run, with Rivard hitting two of his four 3-pointers.
The Tigers (12-9, 5-2) could get no closer than four in the second half. Rivard's trey with 5:36 left pushed the lead into double figures for good.
Ian Hummer's 18 points led Princeton.