Britain got off to a solid start in their Group A clash, with Chicago Bulls star Luol Deng (pictured) in superb form, and looked set to pull off a shock as they outscored Lithuania 18-5 in the third quarter to pull 57-54 ahead.
But the home side pulled clear in the final quarter as Rimantas Kaukenas and Sarunas Jasikevicius made key shots, and Deng's 25-point-haul was in vain.
2003 winners Lithuania looked lethargic for long spells against Britain before waking up in the final quarter, as a lack of depth in their British roster allowed the home side to turn the tide.
"I am glad we found the strength to pull ourselves together, Deng is a good player but one player cannot win a game and I am glad that we won it as a team because they made it difficult for us," said Lithuania guard Martians Pocus.
It was a familiar story for Britain coach Chris Finch as team again came close to beating higher-ranked team before falling short.
"They won a game that came down to making shots," he said.
"I thought we out-fought, out-hustled and out-played them for a lot of the game, but we couldn't out-shoot them, which is what they do very well and it won them the game.
"We lost our last warm-up game against Latvia but that game was an aberration, we were much better here.
"Our lack of depth and experience shows at times, we just need to stay in games and well win our fair share."
Elsewhere in Group A heavily-fancied Turkey smashed Portgual 79-56 while defending champions and hot favourites Spain edged Poland 83-78, with Pau Gasol scoring 29 points.
The 31-year-old power forward, who steered Spain to the 2009 title in Poland, stepped up with some crucial plays in the last two minutes when their unfancied rivals threatened to stun the favourites in the 24-team Eurobasket tournament.
France point guard Tony Parker was the day's other top performer After driving his team to a roller coaster 89-78 win over Latvia in Group B.
The big winners were 2009 runners-up Serbia, who saw off former champions Italy 80-68 in the same group.
Spain seemed to be cruising after Gasol scored 11 of their opening 13 points but the stubborn Poles refused to lie down and forced a dramatic finish on the back of 19 points from point guard Lukasz Koszarek and 18 by American-born Thomas Kelati.
"We played well for three quarters and then let them back in after we relaxed a bit too much and lost some defensive rebounds," Spain's Italian coach Sergio Scariolo said.
"We showed nerves and our concentration was inconsistent, which is typical when you are under all the pressure to win the opening game of the tournament and the most important thing is that we got off to a good start," he said.
Gasol finished with a game-high 29 points and seven rebounds, having received good support from his younger brother Marc, who had 16 points and seven rebounds, as well as point guard Juan Carlos Navarro who added 23 points.
Parker's 31 points and seven assists helped France beat the brave Latvians after his team trailed throughout the first half.
His lightning speed and superior ball skills put Latvia to the sword after they tormented France with a barrage of three-pointers, having made 11 of 23 shots from behind the arc.
Five of them came from point guard Janis Blums, who excelled and led all scorers with 32 points and six assists.
Forward Boris Diaw chipped in with 14 points for the French, Mickael Gelabale had 11 while centre Joachim Noa and point guard Nicolas Batum added 10 each in a balanced team effort.
Serbia failed to score in the opening four minutes against Italy and trailed 18-10 at the end of the first quarter.
A 39-14 run put the Serbs in control midway through the third period and although Italy got within four points with a 19-6 rally they ran out of steam in the closing stages.
"This was a must-win match for us because it's a tough group and we need all the points we can carry into the second group stage," Serbia's trophy-laden coach Dusan Ivkovic said.
"We made a nervous start and we were taken aback by their set plays but the momentum swung our way as soon as we were able to impose ourselves with a team effort and hard work," he added.
1993 champions Germany cruised to a 91-64 rout of Israel thanks to 25 points from their talismanic forward Dirk Nowitzki, who ran the show throughout the one-sided contest.
Having led the Dallas Mavericks to their first NBA title in June, Nowitzki returned to action in grand style and gave the Israelis a roasting at both ends of the court as did his team mate Chris Kamas, who scored 18 points to go with 10 rebounds.
"I felt very well on the court and it was good to win the opening game in such emphatic fashion," Nowitzki told Germany's Sport 1 television.
"We expect to improve as the tournament progresses and we'll certainly have to put in another good performance against Italy on Thursday because they are a really good team," he added.
Montenegro, a tiny republic on the Adriatic with a population of just 650,000, enjoyed their first taste of success in a major event as an independent nation with a 70-65 overtime win over fellow former Yugoslavs Macedonia.
Forward Vladimir Dasic was instrumental in their victory with 20 points and 16 rebounds.
Greece's Nikolaos Zisis and Nick Calathes got 13 points each to give the 2005 winners a 76-67 win over Bosnia in Group C.
Russia, who won the title in 2007, laboured to a 73-64 win over neighbours Ukraine in Group D, where Slovenia also had to dig deep to carve out a 67-59 defeat of Bulgaria.