Serbia also maintained a perfect record with an 89-80 defeat of Israel while former European champions Italy kept alive their hopes of reaching the second stage after centre Andrea Bargnani inspired a 71-62 win over Latvia.
Hosts and 2003 winners Lithuania won a see-saw battle against Turkey 75-68 in Group A, where holders Spain cruised to an 86-69 win over Britain.
Germany forward Dirk Nowitzki, who led the Dallas Mavericks to the 2011 NBA title, drew first blood in his personal battle against Parker in the Group B game, scoring seven of his team's first nine points to give them an early 11-6 lead.
Great Britain rolled aside by powerful Turkey
But it was Parker, himself a triple NBA champion with the San Antonio Spurs, who stole the show after he came to life and stunned the Germans with an irresistible offensive arsenal.
He finished with 32 points, including 15 in the third quarter, scoring from lay-ups through a packed German defence as well as from long range.
Shooting guard Nicolas Batum added 14 points for a French team which held Nowitzki to 20 points after he made just five of his 13 shots from the field.
"We struggled in the second half and found it difficult to get the ball to the basket and keep up with the French, while Parker produced a paramount achievement at the other end," Nowitzki told Germany's Sport 1 television.
Italy, the winners of two titles and four times the runners-up, were staring at early elimination from after trailing Latvia at halftime as they relied almost entirely on Bargnani to keep them afloat in Group B action.
The Toronto Raptors centre responded with a heroic solo effort, scoring a tournament-high 36 points along with seven rebounds to give his team a fighting chance of reaching the second group stage.
The Italians need to win their remaining two preliminary stage games against France and Israel and hope that other results go their way if they are to advance to the top 12, featuring two groups of six.
"It was very important to win and stay in contention after the opening two defeats, we are all exhausted after playing three games in as many days but also overjoyed that we have finally put some points on the board," said Bargnani.
"We have now rekindled our hopes of not just winning our next two games, but playing to the best of our abilities because we know we can improve."
Serbia trailed by 12 points midway through the third period of their Group B match when an on-court skirmish appeared to ignite their comeback against a plucky Israeli side.
Forward Dusko Savanovic poured in 24 points, centre Nenad Krstic scored 18 and Marko Keselj added 15 as the trio collected seven rebounds apiece for the Serbs.
Spain followed their opening wins over Poland and Portugal with a comfortable defeat of Britain in which Pau Gasol and his younger brother Marc combined for 39 points.
Los Angeles Lakers centre Pau scored 21 while Memphis Grizzlies forward Marc chipped in with 18 against one of the tournament's underdogs, whose Chicago Bulls forward Luol Deng had 25 points, including a three-pointer from midcourt.
The first real test of Spain's credentials will come on Sunday, when they clash with Lithuania in a mouth-watering contest between the event's top two contenders.
Power forward Ersan Ilyasova scored 10 first-quarter points as Turkey led 35-32 at halftime in Panevezys but Lithuania, roared on by a passionate home crowd, turned the tide after the interval with a balanced team effort.
"We were good defensively, we fought for each and every ball and left everything out there on the court," Lithuania's forward Paulius Jankunas said after contributing with seven points and two assists.
"We usually struggle in the third quarter and therefore decided to play it more aggressively this time."
Spain defend Eurobasket title
Spain to meet France in final