Seibutis hit two consecutive 3-pointers to open a 63-56 lead with 4:45 remaining in the game and Lithuania, a three-time Olympic bronze medallist , never trailed again.
Britain sent the home fans into a frenzy by notching its first win in men's basketball since the 1948 London Games, beating China 90-58. France made sure it can finish no worse than third in Group A by beating Nigeria 79-73 behind Nicolas Batum's 23 points.
Earlier, Patty Mills hit a 3-pointer on the buzzer to give Australia an 82-80 win over Russia that meant little for either team.
"It's one of those shots you dream of making the at the Olympic Games and to do it against a good team like Russia is great," said Mills, a guard who plays for the San Antonio Spurs in the NBA.
Big plays by captain Amine Rzig, who hit all three of his 3-point shots and finished with 17 points, helped Tunisia take a 54-50 lead after three quarters.
But Simas Jasaitis began the rally with a 3-pointer, Darius Songaila had a three-point play and Jasaitis made two free throws to put Lithuania ahead by one.
Seibutis then stepped up with his consecutive 3s and Lithuania, which lost a narrow 99-94 decision to the United States in its previous game, finally pulled away.
Tunisia had a chance to advance with a win and played hard until running out of steam late in the game. Mantas Kalnietis had a 3-pointer down the stretch and hit a pair of free throws to secure the win.
Songaila, who made the last two free throws of the game for the final score, finished with 13 points, and so did Sarunas Jasikevicius. Rzig led Tunisia (0-5) with 17 points.
In the quarterfinals, Lithuania will play Russia, which was assured of the top spot in Group B even before Monday's game against Australia.
Kieron Achara scored 16 points to lead Britain, which had not qualified for any other Olympics since 1948 and only got a place again at home as the host.
In 1948, Britain beat Ireland for its only win, 46-21. It was beaten at those games by China 54-25.
Australia (3-2) could do no better than fourth and is now scheduled to play either the heavily favoured Americans or Argentina, who play for first place in Group A.
Australia led for most of the game but Andrei Kirilenko had a three-point play and Mills missed a 3-pointer with less than a minute to play. Vitaliy Fridzon made two free throws with four seconds on the clock to put Russia up 80-79.
But Mills got the ball at the top of the key and sank his winner as time expired.
"We knew he was going to shoot it and he made a great play," said centre Sasha Kaun, who led Russia with 18 points.
Alexey Shved and Kirilenko had 13 each. Kirilenko sat out the final minute with a cut above the left eye.
"This game will be forgotten when it comes to the next game. The next game is what is really important," Fridzon said.
Russia's American coach David Blatt said his team was not sharp enough because the game meant little.
"But Australia played great and I give them credit for that," he said.
Joe Ingles led Australia with 20 and Mills finished with 13.
Batum nailed a 3-pointer to put France up 65-62 and the French (4-1) never trailed again after Nigeria had battled back from an 11-point halftime deficit.
The Portland Trail Blazers standout hit two more 3s down the stretch. His 3-pointer with 2:38 to play gave France a 75-68 lead and he drained another for a 79-70 advantage. Batum also had six rebounds.
Boris Diaw, who plays for San Antonio, scored 10 points for France. Spurs guard Tony Parker had seven assists in 21 minutes for France.
Chamberlain Oguchi went 8 for 14 from 3-point range to finish with 35 points for Nigeria.