Andi Herzog's men were second best in a lacklustre first half at the Samy Ofer Stadium, with the visitors on the front foot throughout.
Slovenia started the match with the high press, denying Israel time and space on the ball.
A cagey opening resulted in several misplaced passed, and Slovenia looking dangerous on the counter-attack.
Their high energy levels and work-rate were rewarded three minutes into the second half when striker Andraz Sporer capitalised on hesitancy in the Israel defence to slip the ball past goalkeeper Ariel Harush.
Israel supporters feared the worst, with Slovenia's highly regarded goalkeeper Jan Oblak having already produced one brilliant save, on top form.
But Israel trailed for only seven minutes as Eran Zahavi showed great composure to find the bottom corner.
Key midfielder Beram Kayal was forced off injured with 30 minutes remaining, and Israel lost their rhythm, with able to find a winner in the closing stages.
Israel has never qualified for the Euro finals and if this performance is anything to go by, their wait will continue. But they will be hoping to register a first win at home to Austria on Sunday.
ISRAEL: Harush, Dasa, Taha, Yeini, Ben Harush, Tawatha (sub: Cohen 77), Kayal: (sub: Solomon 63), Peretz, Natchko, Kayal, Dabour, Zahavi
SCORER: Zahavi
BOOKINGS: Peretz, Natchko, Dabour
SLOVENIA: Oblak, Jokic, Mevija, Struna, Stojanovic, Krhin, Kurtic, Verbic (sub: Bijol 90), Zajc (sub: Crnigoj 60), Ilicic, Sporar (sub: Bohar 85)
SCORER: Sporar
SCORER: Jokic
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MATCH STATS
SHOTS: Israel 7, Slovenia 17
On target: Israel 4, Slovenia 7
CORNERS: Israel 4, Slovenia 8
OFFSIDE: Israel 0, Slovenia 3
FOULS: Israel 13, Slovenia 9
CARDS: Yellow - Israel 3, Slovenia 1
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GROUP G STANDINGS
1. FYR Macedonia Pl. 1, W. 1, Pts. 3
2. Poland Pl. 1, W. 1, Pts. 3
3. Slovenia Pl. 1, W. 0, Pts. 1
4. Israel Pl. 1, W. 0, Pts. 1
5. Austria Pl. 1, W. 0, Pts. 0
6. Latvia Pl. 1, W. 0, Pts. 0
