Bale has found himself the main scapegoat for Real's struggles in 2015, with Spanish media and supporters alike criticising the forward, who had his car damaged following the recent Clasico defeat to Barcelona.
However, Bale showed no ill-effects in Saturday's clash in Haifa as he set up Aaron Ramsey to head home the opener and give Wales a deserved first-half lead.
The former Tottenham man doubled the lead after the break with a superb free-kick, before Israel's hopes were all but ended when Eitan Tibi was sent off for fouling Bale - having also committed the foul that led to his first goal.
Bale capped a fine outing by sweeping home the third, as Wales inflicted Israel's first defeat of their qualifying campaign and maintained their own unbeaten record to boost their chances of reaching a first major tournament since 1958.
Bale signalled his intentions early and was at the heart of Wales' efforts going forward, including a wasted gilt-edged chance to take the lead in the 19th minute.
The hosts lost Group B's top scorer Omer Damari to injury and they were dealt a double blow on the stroke of half-time.
Hennessey's long punt down field was missed by home defenders and Bale nodded into the path of Ramsey, who timed his run into the area to perfection to loop his header over Ofir Marciano.
A minute later Tibi's bodycheck on Bale resulted in a second booking as Israel began to unravel.
A third goal duly arrived in the 77th minute, dazzling footwork from Ramsey left the Israel defence bamboozled and he teed up Bale to drill home into the right-hand corner – giving the 25-year-old a much-needed confidence boost before returning to Madrid.
