France were comfortably the better side throughout the match, but did not score until Wilson Palacios conceded a 43rd-minute penalty that also earned him a second yellow card. Benzema converted from the spot and rifled home a second after 72 minutes, his goals split by his part in the World Cup's first ever affirmative use of goalline technology.
Luis Fernando Suarez, the coach of Honduras, raged on the sidelines, but his fury was both in vain and misplaced, the ball having crossed the line . . . just. The Real Madrid striker's first-time shot had clattered the woodwork only to be fumbled on the rebound by keeper Noel Valladares, with the GoalControl system awarding the goal amid some initial confusion.
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.
The favourites wasted no time setting the pace, with Antoine Griezemann and Mathieu Valbuena both impressive.
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.
Benzema fired home to make it 1-0, and what might have been his second went down as an own goal, Valladares palming fractionally over the line after the striker's powerful shot bounced back across goal off the inside of the post.
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.
But Debuchy's long-range drive then fell kindly for Benzema, who fired home an unstoppable shot.