France, world champions in 1998 and finalists last time out, eventually shaded proceedings at a packed stadium before silencing the home crowd when Anelka's 71st minute shot spun cruelly in off defender Sean St. Ledger and then the post.
Giovanni Trapattoni's resolute Irish side will not be totally dispirited, having at least kept the tie alive going into Wednesday's deciding match hoping to overturn the deficit to reach their first World Cup since 2002.
"I feel we are only halfway through. The objective is to qualify," France coach Raymond Domenech told a news conference.
"There are 180 minutes. Ninety to go. The Irish played very well and are very much able to react so we must be vigilant."
Ireland captain Robbie Keane added: "The one (chance) that counted has cost us (but) they got lucky with that goal which was a deflection. We have to believe we can go there and win."
In an even first half, striker Andre-Pierre Gignac, who had averaged a goal every second game in his previous eight France appearances, found the net early on after a lapse by Richard Dunne but his finish was correctly ruled offside.
A second Irish mistake deep in their own half, this time from midfielder Glenn Whelan, gifted Yoann Gourcuff an opportunity from distance but his shot skidded tamely into the arms of goalkeeper Shay Given.
FIRST CHANCE
Ireland's first chance fell to Keane whose close range effort was stopped by France keeper Hugo Lloris before Liam Lawrence's follow up in front of an open goal was deflected wide.
Another flag from the linesman would have ruled either effort out for a foul in any case despite France midfielder Alou Diarra appearing to handle in the box.
Ireland continued to press, playing more of a passing game than they had during their unbeaten group campaign, and Keith Andrews should have done better when he fired wide from outside the box two minutes later.
The last meaningful opportunity of a free-flowing first half fell to France captain Thierry Henry, benefitting from a mistake by Andrews, but the Barcelona striker shot was well off target.
Within minutes of the restart, Ireland caused consternation in the French area from a corner, one of their biggest attacking threat, but another strange decision from the linesman put a stop to the ensuing game of ping pong.
However, the visitors began to find some space with Lassana Diarra sending a scorching half-volley past Given's left hand post from more than 25 metres before Anelka was afforded space to have another shot from distance.
France, without influential playmaker Franck Ribery for both legs through a knee injury and fellow midfielder Jeremy Toulalan for at least this one with a hernia problem, were then unlucky not be handed a penalty after 68 minutes.
Following another slip from central defender Dunne, France left back Patrice Evra nicked the ball past Given but the subsequent contact was adjudged to have been Evra's doing.
Anelka struck decisively three minutes l
