New Chelsea striker Andriy Shevchenko's 71st-minute penalty sealed victory and a place in the last 16 for Ukraine who finished in second spot in Group H behind Spain.
Tunisia finished the group in third spot ahead of Saudi Arabia who were beaten 1-0 by Spain.
The Blues midfielder played for 90 minutes for the Carthage Eagles before being substituted in injury time with what looked like a leg injury.
Tunisia 0-1 Ukraine .. For a full match report .. CLICK HERE