Sergio Ramos gave Spain a first half lead that the World and European champions never looked like defending in an uncustomary nervy second-half performance.
In a game of few chances Hugo Lloris saved a first-half penalty from Cesc Fabregas to keep the French in the game.
The draw brings to an end Spain's incredible run of 24 consecutive wins in qualifying matches that stretches back to 2007, and puts both sides level at the top of the group on seven points, three ahead of Georgia.
Spain had never lost in nine previous international matches in Atletico Madrid's Vicente Calderon stadium, but they were made to fight until the very last minute and it was almost inevitable when Franck Ribery found space on the left to cross for Giroud to level.
Ribery was dangerous all evening especially in a second-half where Spain had to shuffle their defence due to an injury to Alvaro Arbeloa.
France coach Didier Deschamps afterwards insisted that a first-half effort ruled out for offside against Jeremy Menez should have been allowed to stand.
"We stayed calm despite this setback and played our game and deserved our equaliser which I have to say was a very good goal. In fact we could have equalised before we did, we had more chances than Spain in the second-half.
"I have always believed in the quality of my side and our ability to achieve the objective of getting to the finals in Brazil," he said.
Spain coach Vicente del Bosque was pragmatic about the result and his sides chances of qualifying.
"We controlled the game in the first-half but lacked a bit in the final third. We then seemed to tire and let them back in later on. We have five matches left, our return game in France will be important but we can't forget the other sides," he said.
Del Bosque had started without a recognised forward, with Fabregas playing in the 'false nine' role, a tactic employed since Spain successfully defended their European title in June.
Spain suffered an early setback when David Silva limped off, after what looked to be an innocuous challenge, to be replaced on 12 minutes by Arsenal's Santi Cazorla.
The substitute made an immediate impression with the first shot of the evening two minutes later that was comfortably saved by the French captain Lloris.
Spain continued to dominate the opening period and won a succession of corners without punishing their opponents until the 25th minute when Ramos was given the time and space to head against the right-hand post.
The Real Madrid defender appeared to despair at his near miss before composing himself to finish coolly a moment later when Pedro Rodriguez delivered a pass directly back into the goalmouth that Lloris failed to clear.
In the 35th minute Benzema raced onto a Franck Ribery cross and forced Iker Casillas in Spain's goal into his first action of the evening.
Pedro then swept a ball out wide to Arbeloa who crossed from the right and when it fell back to Pedro in a more advanced position he was felled by Arsenal defender Laurent Koscielny and the German referee Felix Brych had no hesitation to point to the spot.
However Lloris second guessed Fabregas to save well to his left and he was the hero again two minutes later when he made a double save from Pedro and then Fabregas.
Somehow the French escaped to the dressing room only a single goal in arrears.
Spain were forced into another change early in the second period when Arbeloa limped off to be replaced at right-back by Juanfran.
France saw their chance and looked for a way back into the game.
Ribery went close with a long range effort before Benzema was dispossessed with a timely interception by Sergi Busquets as he bore down on goal.
At the other end Xavi Hernandez was slow to react in the area when put clear by Pedro then Ribery caused havoc in the Spanish defence with a whipped cross that Casillas pawed clear.
Next it was Benzema who went clear on the left but no Frenchman could get on the end of his cross and when Xavi lost the ball with an unusually weak pass a quick French break saw substitute Moussa Sissokho volley over a Benzema cross.
Del Bosque had seen enough and shuffled his pack to give Fernando Torres the final 15 minutes on his first return back to the stadium where he began his career.
The World Champions however continued to give an edgy performance, giving away possession on countless occasions and it was no surprise when the equaliser came from the head of the late substitute Giroud with virtually the last touch of the game.