Pops Mensah-Bonsu led Great Britain with 21 points with Ogo Adegboye and Dan Clark both adding 13 each.
After a slow opening, Great Britain edged ahead 9-8 and maintained their one point lead to end the first quarter, up 16-15.
GB then pushed their lead to 30-23 mid-way through the second before allowing the Tunisians to end the second on a high, but despite that, the Brits still had a 37-34 advantage at the half.
Tunisia started the third strongly, eventually taking the lead at 51-49 before GB hit back, ending the third quarter up 61-57.
Great Britain though collapsed in the fourth, allowing Tunisia back into the game as they snatched the victory.
Salam Majeri led Tunisia's scoring with 16 points.
Great Britain's men complete their pre-Olympic programme against Belgium on Sunday night.