Turning Point: Great Britain only led 29-24 with six minutes to go in the first half when they stepped on the accelerator and went on a 15-6 run.
Game Hero: Great Britain's Luol Deng had 21 of his 31 points in the first half. He also pulled down 10 rebounds, dished out four assists, blocked one shot and got one steal.
Stats Don't Lie: Great Britain scored 15 points from Portugal's 13 first-half turnovers. Portugal were 20 of 65 (31%) from the floor while Team GB finished 31 of 72 (43%).Luol Deng poured in 21 of his game-high 31 points in the first half to fire Great Britain to their first win in Panevezys.
Chris Finch's men pulled away in the second quarter and went on to claim an 85-73 win.
It is Great Britain's first win in a leading international basketball tournament.
"I will always remember this win as it is my first at a EuroBasket," said Deng, who also pulled down 10 rebounds, dished out four assists, blocked one shot and came up with one steal.
"I think we showed today that we have a great future ahead of us."
Team GB also got a big contribution from Mike Lenzly, who finished with 17 points.
Despite Portugal missing their first seven shots, they went into the second frame with the game knotted at 16-16.
The game remained close but not for long.
Portugal trailed just 29-24 with six minutes to go in the first half when Great Britain went on a 15-6 run to take command.
Mario Palma's men cut the deficit 46-39 midway through the third quarter but were held to just six points for the remainder of the frame.
Portugal never stopped fighting and closed the gap to 68-61 with 4:32 to go but got no closer.
Great Britain's Robert Archibald made his debut in the tournament after missing the opening three games through illness, and the big center contributed with three points, four rebounds, two assists and one blocked shot.
Carlos Andrade led Portugal with 24 points and 10 boards.
Great Britain end their tournament against Poland on Monday while winless Portugal take on tournament hosts Lithuania with nothing to play for but pride.