The Bobcats (14-11, 5-6 Mid-American Conference) led 40-37 at halftime, but the Chippewas (11-12, 6-5) pulled within one point on Brandon Ford's layup with 14 minutes to go.
The Bobcats then went on a 13-2 run and led 64-52 on Bassett's 3 with 10:27 left.
Ohio led by as many as 79-63 on Washington's free throws with 3:39 remaining.
Washington made a career-high 14 free throws out of 19 attempts as Ohio was 35 of 48 from the foul line (72.9 percent).
The Bobcats shot 57.1 percent in the second half (12 of 21), compared to 31.6 percent shooting (12 of 38) by the Chippewas after halftime.
Robbie Harman had a career-high 31 points and nine 3-pointers for Eastern Michigan. Harman became the school's all-time leader in 3s with 208.