Benzema bagged a brace himself, while a bizarre own goal by Honduras goalkeeper Noel Valladares saw goal line technology used for the first time in a World Cup to confirm the ball had crossed the line.
In a bruising encounter, Honduras were reduced to 10-men after Wilson Palacios charged into French midfielder Paul Pogba seconds before the break in a challenge that had him sent-off for a second booking. Benzema smashed home the resulting penalty to give France a lead they deserved having dominated the first 45 minutes.
Three minutes into the second half, Benzema stole past the defence to shoot across goal with his shot coming back off the far post, rolling along the line and going in off Valladares.
Benzema struck again with 18 minutes left when he shot from a narrow angle on the right past Valladares and into the roof of the net, earning a rendition of "La Marsellaise" from the red, white and blue clad French fans.
The result will go a long way towards helping the 1998 champions banish the ghost of their disastrous campaign in South Africa, when the players mutinied against coach Raymond Domenech and returned home in disgrace.
It also signalled that Benzema could be one of stars of the tournament.
Coach Didier Deschamps will take heart that the French looked composed and did not get flustered when the goals were slow to come, although arguably they could have banged in a few more in the second half against the reduced Honduran side.
On top of Benzema's performance, defender Mathieu Debuchy looked impressive, notably for his forays up the right.
"I think it is a marvellous start for us. It was a very important match indeed. Honduras played with high quality and defended aggressively and that was very complicated for us even though we hit the bar twice," Deschamps said.
The penalty and sending off changed the situation, he said.
"We scored three goals, we could have scored even more goals but it was a good start for our team."
The match, played before more than 43,000 fans in an almost full Beira Rio stadium, was the first between the two teams.
Despite accusations that Honduras were a thuggish side, France dished it out too and the first yellow card was handed to left back Patrice Evra after he body-checked young midfielder Andy Najar in the 7th minute.
France dominated almost from the start and might have opened their account earlier.
A shot by midfielder Blaise Matuidi was tipped on to the crossbar by Valladares in the 15th minute and Les Bleus rattled the bar again in the 23rd with a header by Antoine Griezmann from Evra's cross.
The tackles were going in fast and hard and matters came to a head in the 28th minute when Palacios and Pogba tangled on the ground, the veteran Honduran appearing to stamp the Frenchman and receiving a kick in return. Both were given a yellow card but the incident was to have its denouement later.
Just before the break, Palacios clattered into Pogba in the penalty area. Given his second yellow card, he made an ignominious walk off the field and Benzema drilled in the penalty hard and high.
After that, the game was up for the Hondurans.
Three minutes into the second half, Benzema's shot cannoned off the post and back across the face of goal before Valladares inadvertently pushed it towards his own net.
Despite his desperate efforts to scramble the ball clear, the referee awarded the goal with the aid of the technology. Initially, it was credited to Benzema then logged as an own goal.
"I don't know if it is good to have goal line technology because football is like that, sometimes you don't know whether the ball was in or not but the essential thing is that it counted and we won," Benzema said.
"I'm happy, I'm proud the most important thing is the victory."
The win puts France in a good frame of mind for the tougher challenge against Switzerland next Friday.
Honduras will have done nothing to lessen their reputation as perennial underdogs with a nasty bite. They will try to salvage some pride and clock up their first ever World Cup win when they tackle Ecuador.
Honduras coach Luis Fernando Suarez made no excuses for his side.
"They played better than we did. We will have to improve but sometimes it is difficult to play with less players for such a long time especially facing a team that is very well organised." he said.
"The results would have been different if we had our 11 players but these things happen."