Barcelona forward Pedro scored the only goal of the game just before the hour mark to help the world champions leapfrog the French into first place in Group I.
Spain top the section with 11 points and took a massive step towards qualifying for World Cup 2014 in Brazil with the win.
The visitors took the initiative in the early going and were almost rewarded for their attacking endeavor in the fifth minute, but Xavi inexplicably missed the target from just six yards out.
Xavi had another opportunity to open the scoring moments later but once again missed the net when he should have done better.
France was clearly on the back foot in the first half and was lucky not to concede a penalty when Pedro took a tumble in the box but the referee waived away his protests.
Spain had to be content with a scoreless draw at the half-time interval.
Andres Iniesta almost gave Spain the lead, but France goalkeeper Hugo Lloris did well to tip the Barca man’s shot over the bar.
However, Lloris was powerless to stop the visitors from taking the lead when Pedro tapped in Nacho Monreal’s cross in the 58th minute.
Spain had a precious 1-0 lead and things went from bad to worse for France when Paul Pogba was shown his second yellow card.
The 10-man hosts could not find a way past the Spanish defence and now sit one point behind the European champions.
Spain coach Vicente del Bosque hailed his team’s performance and was relieved to have secured the win at the Stade de France.
“This is a very important three points,” he stated. “It helps the conviction we have in our ideas. Everyone has doubts at times.
“When they went down to 10 men it should have been easier for us but this is when we had the most problems. The team played like men today.”
Spain are the defending European and World Cup champions and will look to make history by winning its fourth major tournament in a row.