The visitors held a shock 10-0 lead at half-time thanks to tries from Daniel Chiha and John Koborsi.
Chris Salem raced 80m for a brilliant solo try to put the Cedars back in front until Littler's effort, converted by Chris Bridge, saved Irish blushes.
Ireland coach Andy Kelly had mixed emotions after a pulsating game at Tolka Park.
"I'm disappointed and relieved," he said. "We looked like we would get nothing but one final heroic effort saved us."
"We had targeted four points from these opening rounds but we will settle for three and we are still hoping to take our place in the finals," he added.
The match was the final qualifier of 2006 and leaves everything still to play for in the return rounds next autumn.
Lebanon coach George Elias said: "It's a great result for us in a game that could have gone either way but the passion of the Lebanese pulled us through despite having such a young squad."
Ireland: (0) 18 Tries: Grix, Tandy, Littler. Goals: Bridge (3)
Lebanon: (10) 18 Tries: Chiha, Koborsi, Salem. Goals: Salem, El Masri (2)
Ireland: Scott Grix, Damien Blanch, Stuart Littler, Tony Stewart, David Dodd, Chris Bridge, Bob Beswick, Ryan Tandy, Phil Cantillon, Paul McNicholas, Mick Cassidy, Ged Corcoran, Dave Allen. Subs (all used): Garreth Haggerty, Alan Robinson, Steve Gibbons, Steve Nolan.
Lebanon: Samer El Masri, Adham el Zbaibieh, Daniel Chiha, Frank Samia, Chris Salem, Anthony Farah, Jai Ayoub, Charles Farah, George Ndaira, Charlie Nohra, John Koborsi, Khalid Deeb, Philip Takchi. Subs (all used): Allen Soultan, Ali Karouche, Amin Maassarani, Rudi Hachache.
European Group 2 Qualifier Standings: Ireland 1 win, 1 draw, 3 points Lebabnon 1 win, 1 draw, 3 points Russia 2 losses, 0 points
Return matches Oct-Nov 2007, top team qualifies for ten-team World Cup Finals in 2008, second team goes to repecharge round to contest final qualifying spot against Samoa, USA and either Wales or Scotland.