By Rob Dugdale
BBC Sport at the NIA, Birmingham
Mensah-Bonsu scored 15 points and was again dominant in defence
Luol Deng hit 29 points as Great Britain continued their winning run in European qualifying Group D with a 82-74 win over Bosnia-Herzegovina.
GB were the better side in the second half after going in 41-41 at half-time against well-organised opponents.
Chris Finch's team stay top of EuroBasket qualifying group D after three of their six games.
The news was less good from the women's team, who lost 74-72 at home to Germany and drop into the relegation play-offs.
GB relied on Deng to keep them ticking over in the first half and he responded with 16 points as Bosnia proved stubborn opponents.
In the third quarter, the hosts silenced the noisy elements of the visitors' support by holding Bosnia scoreless for five-and-a-half minutes, taking a 58-43 lead.
Bosnia staged a short revival at the start of the fourth quarter with a 6-0 run but Deng and Pops Mensah-Bonsu re-established control as GB hit nine unanswered points to put the outcome beyond doubt.
Mensah-Bonsu finished with 15 points and 11 rebounds.
"We were allowing them to dictate the tempo in the first half," said GB playmaker Flinder Boyd. "In the second half we came out and played like we did on Saturday.
"It was similar to the game we played against them in Turkey - Bosnia are a team you can't underestimate because they are more athletic and skilled than they look.
"The three from Luol on the wing (in the fourth quarter) was a big shot - that was the dagger in the heart, so to speak."
GB coach Chris Finch was pleased with the side's second-half performance.
"It was our goal to really force the ball to Luol early and get him involved, rather than the game against the Czechs," he said.
It was our goal to really force the ball to Luol early and get him involved
"I thought he took really good shots in the first. I was pleased with the offence for the most part."
GB now move on to the return match with Israel in Liverpool on Saturday, knowing a win will keep them top of the group ahead of their final two qualifiers in the Czech Republic and Bosnia.
Meanwhile, Megan Moody had 18 points for GB's women's team and Johannah Leedham added 16, but it was not enough to hold off Germany, who were led by Anne Breitreiner's 24 points.
Moody's three-point attempt in the last three seconds missed, meaning Mark Clark's team must now concentrate on avoiding relegation next year.