The 23-year-old Pecherov, who was traded from the Washington Wizards to the Minnesota Timberwolves in June, also grabbed an eye-popping 17 rebounds in Friday's game.
Ukraine dominated the boards, out-rebounding Hungary 59-33.
Hungary led 45-32 with 7:16 remaining in the third quarter but didn't press home the advantage.
Instead Ukraine battled back and took a 57-56 lead two minutes into the last quarter on a jump shot by Sergio Gladyr.
They didn't go in front for good until midway through the period, though, when Dmytro Gliebov split two free-throws and Pecherov followed with a thunderous dunk.
David Vojvoda's three-point play trimmed the deficit for Hungary to 65-64 with 3:32 remaining, but Pecherov responded with a three-pointer and then hit two free-throws as Ukraine took command for good.
"I am happy because despite all the difficulties we managed to emerge victorious. I told my players before the game that if we don't allow more than 70 points, we will win. It's a problem for our team to play well for the whole 40 minutes and that's the reason we were forced to come back once again (in this game)."
Oleksiy Pecherov, player Ukraine:
"I am happy we won. We showed character in the second half and got such an important victory. We now have to try to win the game on the road and will have to win the last game here at home. I am also glad we overcame our horrible 17 of 0 first-half shooting from behind the ark and found our rhythm."