France, the runner-up two years ago, got 18 points from Tony Parker but faded as Benzing scored the last five points of the game for the second youngest team in the 24-nation tournament.
"Nobody believed in us but we all believed. This is a great victory," Germany captain Heiko Schaffartzik said.
Spain, which beat France in the final two years ago, limited Croatia to three points in the final quarter and began its bid for a third straight title with a crushing 68-40 victory.
Marc Gasol had 14 points and 11 rebounds, Rudy Fernandez added 15 points, Jose Calderon had 13 and Ricky Rubio had seven assists to go with seven points as Spain dominated the Group C match in Celje, outscoring Croatia 19-3 in the fourth.
When Calderon nailed a 3-pointer for a 47-29 lead in the third quarter, the game was decided and Spain cruised home.
Spain is seeking to become the first team to win three consecutive European titles since Yugoslavia in the 1970s. The Spaniards are playing without stars Pau Gasol, Serge Ibaka and Juan Carlos Navarro.
Bojan Bogdanovic had 12 points for Croatia.
Russia, bronze medallist two years ago, also lost, going down 76-69 to Italy, which got 25 points from Luigi Datone. Host Slovenia eked out a 62-60 victory over the Czech Republic in Group C.
Germany finished the first quarter of the Group A game with a 10-0 run to take a 27-14 lead and France did not lead until the start if the fourth quarter. Trailing by three, Germany pulled even on Lucca's Steiger's 3-pointer and the shooting guard made another one to put Germany ahead for good. Parker then scored with a layup but Benzing nailed a 3-pointer and made two free throws with 13 seconds left as Nicolas Batum missed two back-to-back 3-point attempts.
"They made the big shots and deserved to win," Parker said.
In Group B in Jesenice, Montenegro edged Macedonia, a semifinalist two years ago, 81-80, with American-born guard Tyrese Rice nailing two free throws with 10 seconds remaining. Bo McCalebb, another American-born guard, led Macedonia with 23 points but missed a layup to win the game.
Rice and Suad Sehovic had 16 points each for Montenegro, which overcame the absence of its star big man Nikola Pekovic.
Another American-born guard, Eugene Jeter, also played a key role in Ljubljana, converting a three-point play with three seconds remaining to give Ukraine a 58-57 win over Belgium in Group A. Jeter put in a layup, drew a foul and converted the free throw to finish with eight points. Ihor Zaytsev of Ukraine led all scorers with 16.
"We're very fortunate the way the game turned out from the stand point of having scored only 26 points in first half," said Ukraine's American coach Mike Fratello.
Greece rolled past Sweden 79-51 in Group D.
Earlier, Kyle Johnson scored 22 points and Kieron Achara added 18 with 13 rebounds to lead Britain to a 75-71 overtime upset victory over Israel in the first Group A match.
Also, Finland got 12 points apiece from Petteri Koponen and Sasu Salin to stun Turkey 61-55 in Group D in Koper, while Latvia beat Bosnia-Herzegovina 86-75 in Group B and Georgia defeated Poland 84-67 in Group C.
In Ljubljana, Israel took the lead for the first time in the third quarter but never managed to pull away. Andrew Lawrence made two free throws to send the game into overtime.
A layup by Lawrence gave Britain a 73-71 lead with 16 seconds remaining in overtime. Afik Nissim, who led Israel with 17 points, then lost the ball and Andrew Sullivan sank two free throws to seal the victory.