The match was played at Khalid Bin Mohammed Stadium in Sharjah because of a one-match stadium ban on Lebanon following unruly scenes in their qualifier against Syria in Beirut last year.
But with Palestine also displaced because of the current conflict with Israel in Gaza - they play their first 'home' game against Australia in Kuwait next week - the two sides stood for a minute's silence before the game for the victims of the fighting.
More than 11,500 people have been killed in Gaza since Israel launched its offensive in retaliation for the cross-border attacks by Hamas on October 7 in which 1,200 people were killed and about 240 others taken hostage.
It was the first meeting between the teams and saw a defensive Palestine largely on the back foot as the Lebanese created the best of the opportunities. The first chance of the match came in the 12th minute, but Lebanon captain Hassan Maatouk shot just wide from a long-range attempt.
Atta Gaber had the best chance for Palestine in the first half with a header on the half-hour mark, while Mohammed Saleh and Oday Dabbagh came close to scoring in the second half.
Palestine goalkeeper, 32-year-old Rami Hamadeh, made several crucial saves including one in the 89th minute with his outstretched leg, which led to a pulled hamstrings and a difficult final few minutes.
The top two finishers in each of the nine groups advance to the third phase of qualifying. Asia will have at least eight spots in the expanded 48-team World Cup.