Giannis Antetokounmpo had 40 factors and 13 rebounds, and Khris Middleton made the tiebreaking shot with 40 seconds left within the first additional time Sport 7 in 15 years.
The Bucks held on from there when Durant missed two jumpers, the final an airball with 0.3 seconds remaining.
Middleton added 23 factors and 10 rebounds for the Bucks, who reached the East finals for the second time in three years. They are going to play both Philadelphia or Atlanta in a sequence that begins Wednesday evening.
Durant performed all 53 minutes and compelled OT with a turnaround jumper that was simply inches from being a 3-pointer that might have received it with a second left.
He added 9 rebounds and 6 assists, however did not have sufficient assist with injured Kyrie Irving watching from the baseline and James Harden unable to find his shot after lacking many of the first 4 video games with proper hamstring tightness.
Harden had 22 factors, 9 rebounds and 9 assists, however was 5 for 17 from the sphere.