Defender Mamadou Sakho and Karim Benzema scored a goal each as France beat 10-man Ukraine 3-0 on Tuesday and overcame the odds to reach the World Cup.

Although Ukraine played most of the second half with 10 men, France was already leading 2-0 by then after goals from Mamadou Sakho and Karim Benzema.

Trailing 2-0 after the first leg of their playoff, France opened the scoring with Sakho's first international goal and Benzema finished from close range in the 34th.

Ukraine went down to 10 men when fullback Yevhen Khacheridi was red-carded for fouling Franck Ribery in the 47th and France sealed qualification in the 72nd minute when subsitute Oleg Gusev turned a cross into his own net under pressure from Sakho.

There were delirious scenes at the end as France players rushed off the bench and the Stade de France celebrated.

Bullied all night in Kiev last Friday, the French responded brilliantly in a performance full of bravery, panache and determination.

''It's the magic of football. Four days ago we were bad, very bad,'' France coach Didier Deschamps said. ''Tonight the players were present and I had no doubt they would be.''

The players, under intense pressure in the build-up to the game, grabbed flags and sprinted around the field in jubilation as France avoided the embarrassment of failing to qualify for a major tournament for the first time in 20 years.

Giroud grabbed a microphone and got the crowd singing along to the national anthem as pent-up emotions were well and truly released.

''It was a great, great game. It was important for French football to be in Brazil and we will be,'' Deschamps said. ''When we've got all the ingredients, we can do great things.''

In a match four years ago, 10,000 traveling Irish fans drowned out the home support. But there was no danger of that this time from Ukraine's considerably smaller following.

Pre-match footage on the stadium's big screen showed clips of glory days: the Platini years, the 1998 World Cup and Euro 2000. Perhaps this was an attempt to jog the crowd's memory, a last-ditch plea to get them to rally behind the team. Or perhaps it was a simpler message: ''This is how to win, remember?''

The words to ''La Marseillaise'' then popped up on the screen, offering further encouragement to show their support.

It seemed to have the desired effect as France poured forward and had Ukraine firmly on the back foot from the outset, with Mathieu Valbuena going close with a rising shot and Paul Pogba and Benzema heading over from good positions.

Piatov had kept eight consecutive clean sheets but his resistance was finally broken when Sakho pounced to turn the ball in from close range after Piatov pushed away Ribery's shot from the edge of the penalty area.

Some of the tackling was ferocious, as this time France stood up to the physical challenge after their battering in Kiev.

France went ahead following another dangerous Valbuena freekick. The ball landed to Ribery on the edge of the area and his firmly-hit shot forced Piatov to dive low to his right. The ball span away from him and Sakho was on hand to bury the rebound and Sakho ran toward the home bench slapping his chest with bursting pride.

France had the ball in the net again in the 30th as Benzema angled in Ribery's cross but the goal was ruled out for offside.

Piatov was well beaten when Cabaye's attempted shot deflected favorably into the path of Benzema and he stroked it into the bottom corner.

Moments before halftime, Sakho stretched his leg high to poke the ball away from Roman Zozulya as he was about to shoot and, from the resulting corner, Andriy Yarmolenko's goal-bound hit Mathieu Debuchy's chest.

Khacheridi got a second booking just two minutes after the restart for hacking down Ribery and was sent off.

Ribery was irrepressible down the left, creating chances for Blaise Matuidi and Benzema.

The French bench rose in unison when Gusev turned a cross into his own net. Substitute Olivier Giroud almost made it 4-0 but his point-blank header was superbly saved by Piatov.