The Maccabi Petah Tikva attacker had been on the pitch for only six minutes when he settled matters with a low strike from just inside the box. The win, Israel's second in four days, saw them leapfrog their opponents into third in the Group F table, one point behind leaders Greece, albeit having played one game more.
Maor Buzaglo had an early effort blocked by Genoa defender Kakha Kaladze, before Lior Rafaelov headed a fine cross wide of the target. Buzaglo should have done better from 12 yards shortly after, but his weak shot was comfortably caught by Georgia goalkeeper Nukri Revishvili.
His opposite number, Dudu Aouate, was called into action after 16 minutes when he turned Alexander Amisulashvili's header from a Zurab Khizanishvili free-kick round the post.
Israel were handed a good chance just before the half-hour mark when Akaki Khubutia fouled Elyaniv Barda 20 yards from goal, but Rafaelov sent his free-kick against the wall. The Maccabi Haifa man did far better 10 minutes before the break, though, when he drilled his effort from just outside the box on target, only to be saved by Revishvili.
When Rafaelov won a free-kick four minutes later, he handed responsibility to Bibras Natkho, who fired poorly over from 25 yards.
Georgia had their chances after the restart, with Jaba Kankava and Otar Martsvaladze failing to test Aouate, while Dani Bondarv and Buzaglo were equally wasteful at the other end. But Buzaglo made amends as he played in Ben Haim, who had replaced Natkho moments earlier, to finish from 12 yards for the opener.
More chances followed for the hosts, with Almog Cohen firing over and Kaladze throwing himself in front of an effort from Elyaniv Barda. Georgia could muster little save a clutch of long-range strikes, and they could have slipped further behind a minute from time, but Revishvili smothered Buzaglo's 12-yard shot.