Nigeria led the Tunisians all through with gaps as wide as 15 points, but the Tunisians fought back, narrowing the lead to 2 points in the fourth quarter.
Alade Aminu scored 15 points and grabbed nine rebounds while Ike Diogu added 13 points and 10 rebounds.
Al-Farouq Aminu, who played for the NBA New Orleans Hornets last season, added 10 points and nine rebounds for the Nigerians, who have not lost to reigning African champion Tunisia in international competition since 1987.
The two African sides in the London line-up were both making their Olympic debuts in the Group A round-robin contest. The top four teams in each of two groups advance to the medal playoffs.
Nigeria were the last team to qualify for the Olympics, having beaten the Dominican Republic in the qualifying tournament decider to advance after upsetting Greece earlier in that event.
Only three Nigerian players were born in the African nation. The others, including former NBA San Antonio Spur Diogu, were born in the United States but are of Nigerian heritage.
Tunisian captain Amine Rzig scored 18 points in a losing cause.
The Nigerians seized their largest lead at 29-10 on the way to a 31-15 half-time advantage before Tunisia rallied, scoring 25 points in the fourth quarter and pulling within 56-54 in the final seconds on a Mourad El Mabrouk three-pointer.
Nigeria sank three free throws down the stretch to secure the victory.