The result left Serbia top with 19 points from eight matches, four more than 2006 finalists France, who can still win the group but are not yet assured of a playoff berth with two games left.
Serbia made the brighter start and Gojko Kacar almost gave them a fifth-minute lead with a stinging shot parried by France goalkeeper Hugo Lloris.
LLoris was harshly sent off four minutes later, when Serbia striker Nikola Zigic raced clear into the penalty box and went down after the goalkeeper appeared to make minimal or no contact with him.
Nenad Milijas drilled the spot kick into the roof of the net to give Serbia the lead in front of 55,000 passionate fans, one of whom raced on to the pitch to congratulate Milijas and was swiftly taken away by security stewards.
France soon regained their composure, however, and Thierry Henry tapped in the equaliser in the 31st minute, after Serbia goalkeeper Vladimir Stojkovic spilled a soft low show by Nicolas Anelka from 18 metres.
The home crowd held their breath on the stroke of halftime after Yoann Gourcuff's 40-metre free kick almost caught Stojkovic napping, with the keeper making a last-gasp save to push the ball over the bar.
France enjoyed the lion's share of the possession in the second half but Serbia missed the best chances to snatch the winner against the run of play.
Right back Branislav Ivanovic rattled the crossbar with a thunderbolt from 25 metres on the hour and substitute Milos Ninkovic's shot from 18 metres flew just wide of the far post six minutes later.
The French laid siege to the Serbian goal in the closing stages and only desperate defending by the home side denied the visitors victory.
The Serbians had substitute Danko Lazovic sent off in the 90th minute for dissent, after he was shown a straight red card for complaining to the referee.
Serbia, aiming to qualify for a major tournament for the first time as an independent nation, play Romania at home next month and a win would secure their berth in the finals.
