In a match refereed by Premier League official Mark Clattenburg, Belgium settled first, with Axel Witsel coming close for the visitors inside three minutes, with his drilled shot whistling inches wide of the post.
Belgium forged ahead on eight minutes when an offside-looking Vincent Kompany crossed for Fellani to scramble the ball over the line.
Israel keeper Ofir Marciano was called into attack moments later, producing a smart save to deny Kevin De Bruyne.
Kompany then received the first of two yellow cards after a late challenge on Sahar.
The match was played at a pedestrian pace in the main, and it was Belgium who had the last chance of the half, with Christian Benteke appealing for a penalty after Rami Gershon appeared to block a shot with his arm, but Clattenberg only awarded a corner.
Having failed to register a shot on target in the first half, Israel introduced Tal Ben Haim for the start of the half. And the home team made their intentions clear early on as Bibras Natcho arrowed a speculative effort straight at Courtois, whose evening was about to get busier.
Eran Zahavi was next to try his luck, forcing an acrobatic save from the Chelsea stopper who commanded his box and showed good handling throughout.
The momentum was with Israel as they went in search of an equaliser, without seriously stretching Belgium.
Good link up play on the hour between Sahar and Zahavi saw the latter let fly with a swerving effort that forced another excellent save from Courtois.
The 63rd minute saw the ineffective Eden Hazard's night called to a premature half, as coach Marc Wilmots introduced Tottenham's Nacer Chadli.
The visitors were reduced to 10 men when Clattenburg cautioned Manchester City's Komany for a second time for tugging Zahavi back.
Belgium were forced on to the back foot for the final 27 minutes, but they repelled everything Israel threw at them, with Zahavi producing a series of disappointing set-pieces.
Sahar forced Courtois into another smart save low down in the closing stages as Belgium held on.
The result lifted Belgium above Israel who are next in action when they travel to Bosnia in June, with their hopes of qualification firmly in the balance.
ISRAEL: Marciano, Ben Haim (capt), Gershon, Dgani, Ben Harush (sub: Refaelov), Biton, Natcho, Zahavi, Yeini (sub: Barda), Hemed (sub: Ben Haim), Sahar
CARDS:
Yellow - Dgani, Yeini, Refaelov
BELGIUM: Courtois, Alderweireld, Lombaerts, Kompany, Vertonghen, Witsel, De Bruyne, Fellaini, Hazard (sub: Chadli), Nainggolan (sub: Denayer), Benteke (sub: Origi)
CARDS:
Yellows - Kompany (x2), Alderweireld, Lombaerts
Red - Kompany
GOAL:
Fellaini 8
GROUP B STANDINGS
1. Belgium Pl. 5, W. 3, D. 2, L. 0, F. 13, A. 1, Pts. 11
2. Wales Pl. 5, W. 3, D. 2, L. 0, F. 7, A. 2, Pts. 11
3. Israel Pl. 5, W. 3, D. 0, L. 2, F. 9, A. 6, Pts. 9
4. Cyprus Pl. 5, W. 2, D. 0, L. 3, F. 9, A. 10, Pts. 6
5. Bosnia & H Pl. 5, W. 1, D. 2, L. 2, F. 5, A. 6, Pts. 5
6. Andorra Pl. 5, W. 0, D. 0, L. 0, F. 2, A. 20, Pts. 0
