The game also saw the first successful usage of goal-line technology in the tournament during France's second goal - ruling that Honduras goalkeeper Noel Valladares had pushed the ball over the line in the 48th minute.
Benzema fired a shot off the post and after it appeared that the Honduran keeper had prevented it from going in, the GoalControl system showed that the ball had trickled over the line giving France a 2-0 lead while officially confirming it as a Valladares own goal.
The game was keenly contested and tempers flared when Paul Pogba and Wilson Palacios clashed in midfield, with the Juventus midfielder appearing to kick out at Palacios. Despite the Honduras bench calling for Pogba to be sent off, both players were issued with a yellow card.
Moments before half-time, France were awarded a penalty after Pogba was bundled over in the area by the Stoke City player – with Palacios receiving his second yellow card and subsequent marching orders.
Benzema scored his first of the game after firing the resulting spot-kick into the top-left corner - giving France a richly deserved 1-0 lead before the break.
Les Bleus created numerous chances throughout the game, with both Blaise Matuidi and Antoine Griezmann hitting the bar as Didier Deschamps’ side controlled the match with relative ease.
France’s Benzema was in inspired form and he scored his second of the game twenty minutes from time. After Mathieu Debuchy’s deflected shot fell into his path, the Real Madrid man hit it high into Valladares’ goal – giving France their third goal and a deserved three points.
As well as the three points, France will be just as happy to have departed without serious injury after 90 minutes of late tackles and physical intimidation from their limited opponents.
France wasted no time setting the pace, with Antoine Griezemann and Mathieu Valbuena both impressive.
Griezemann, making his first competitive start, had a fine chance to open the scoring in the sixth minute when he took a poor clearance on the chest and saw his goalbound effort blocked.
Valbuena and Mathieu Debuchy were enjoying plenty of joy down the right and the former's cross caused Valladares to fumble.
Honduras invited pressure with a series of fouls that allowed Valbuena to send a series of testing free-kicks into the danger area.
Blaise Matuidi nearly scored from a half-cleared Valbuena delivery, controlling with his thigh then seeing a powerful shot brilliantly pushed against the bar by Valladares.
France went closer yet in the 23rd minute, Griezemann beating Maynor Figueroa to a Patrice Evra cross and heading against the crossbar.
The game could have changed moments later when Palacios tussled with Paul Pogba, the Honduran guilty of a couple of kicks at his opponent and Pogba retaliating by rashly flicking a leg out.
Both saw yellow cards, with Pogba particularly relieved.
After play resumed France's flow had deserted them, with Benzema beginning to show frustration at his lack of clear opportunities.
Palacios rectified that just before half-time when he barged through the back of Pogba as he shaped to shoot, earning a second yellow card and conceding a penalty - which Benzema converted with ease.
Honduras reshuffled with two changes at the break but shipped a second inside three minutes.
It went down as an own-goal, Valladares palming fractionally over the line after Benzema's powerful shot bounced back across goal off the inside of the post.
Honduras boss Luis Suarez seemed unhappy with the verdict but without good reason.
Amid repeated nasty challenges a third seemed inevitable, but Matuidi spurned a glorious chance shortly after the hour when slotting Evra's pinpoint cross into the side netting.
Benzema then provided it with 18 minutes left.
Debuchy's long-range drive did not make it through a crowd of bodies but fell kindly for the centre forward, who hammered home an unstoppable shot at the near post.