Okolie hit 9 of 11 shots from the field and finished 10 of 10 at the free-throw line. Patrick Steeves added a career-best 20 points for Harvard (7-8, 1-0).
An Okolie 3-point play with 2:14 left in the game capped a 7-0 run to put the Crimson up 70-62. Evan Boudreaux made a 3 for Dartmouth to cut the lead to 73-70 with 43 seconds left, but four Okolie free throws put the game away.
Miles Wright scored 23 points to lead Dartmouth (4-9, 0-1). Boudreaux added 21 points.
The game was 29th straight season that Harvard and Dartmouth have played in the conference opener. Harvard holds a 19-10 edge over the Big Green and is 9-0 under coach Tommy Amaker.