Meijri scored a game-high 22 points and grabbed 15 rebounds, while Michael Roll added 18 points for Tunisia. Aaron Geramipoor had 18, and Hamed Haddadi made 13 points and 11 rebounds for Iran.
Tunisia made 13 three-pointers, which decided the game, reports Xinhua news agency.
"Spain made 17 three-pointers last match against us, and today we made 13. Our players did a great job," Tunisia coach Mario Palma said.
Both sides suffered bitter losses in their opening games two days ago, when Iran was beaten in the last seconds by Puerto Rico and Tunisia lost to Spain by 39 points.
Monday's game started intensely with the two teams tied at 10-10, 12-12 and 15-15. Meijri stood out to hit a three-pointer and led the team to a 9-0 run before Tunisia finished the first quarter leading 29-19.
The Tunis controlled the game well in the second quarter and kept the advantage, leading 44-35 before half time.
Geramipoor scored four points for Iran into the second half, only to see Meijri score a three again. Tunisia increased the lead to 59-48 by the end of the third quarter.
Haddadi and Behnam Yakhchalidehkordi inspired Iran to cut the deficit to only five in the beginning of the fourth quarter. But the Iran' hopes dimmed as Roll and Mourad Mabrouk scored to clinch the victory for Tunisia.
"It is not enough for us to win just one game, we need to win the game against Puerto Rico, then we will reach the last 16 and make it to the Tokyo Olympics," Palma said.
( With inputs from IANS )