Giroud's fine effort after he had been on the pitch a matter of minutes only from Franck Ribery's centre denied the Spanish a 25th straight win in major championship qualifiers but was no more than France deserved after a battling second-half performance.
Striker Karim Benzema had told Monday's new conference he and his team mates would be 11 warriors on the pitch and Didier Deschamps's side put a poor first-half display behind them.
Sergio Ramos had put Spain deservedly ahead in the 25th minute before France goalkeeper Hugo Lloris saved a poorly struck Cesc Fabregas penalty shortly before the break.
France looked a different side in the second half, while Spain were unusually ragged, and the visitors almost equalised several times before Giroud leaped to nod the ball into the corner of the net in the fourth minute of added time.
There was only enough time for Spain to kick off again before the referee blew the final whistle to prompt wild celebrations from Deschamps and his men and whistling and booing from the home support.
Spain, who play away in France at the end of March, remain top of the group, tied with the French on seven points from three matches but ahead on goal difference.
"They pressured us a lot in the second half and we gave them too much space," Spain coach Vicente del Bosque said in an interview with Spanish television.
"But that's not to take anything away from them getting the draw."
A miserable night for Spain was further soured by injuries to playmaker David Silva and right back Alvaro Arbeloa, who had to be replaced in the 13th and 50th minutes respectively.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO Sports and on Facebook at AhramOnlineSports)