France dominated the match from the opening whistle, despite a series of scrappy tackles by the Honduran team seeking its first World Cup win.
Benzema's first goal came from the penalty spot just before halftime after Wilson Palacios was sent off with his second yellow card for charging into the back of Paul Pogba. The Real Madrid striker calmly slotted the ball to the left of Noel Valladares to give Les Bleus a deserved lead going into the break.
With Honduras down to 10 men, France continued to dominate and Benzema created the second goal in the 48th minute the first to be confirmed by goal-line technology at the World Cup.
Benzema latched onto a long ball by Yohan Cabaye and his shot hit the post and came back across goal before Valladares fumbled it over his own line. With the new technology system confirming the ball crossed the line, referee Sandro Ricci gave the own goal despite Honduran protests.
Benzema scored his second in the 72nd, firing in powerfully from inside the area after a long range shot by right back Mathieu Debuchy was blocked.
"It's my first World Cup and I think we're all satisfied with the result," Benzema said. "It was important to win this match."
French keeper Hugo Lloris didn't have to touch the ball until the 31 minute and didn't have to make a save all night.
France looked dangerous from the start, with Blaise Matuidi and Antoine Griezmann both hitting the crossbar before the half-hour mark.
The only downside for the French fans was that the teams' national anthems weren't played before the game because of an apparent malfunction meaning they didn't get a chance to sing "La Marseillaise." FIFA did not immediately give an explanation to why the anthems weren't played.