Real Madrid star Bale has been much maligned by the club's supporters and the Spanish media in recent weeks as the Liga giants have struggled for form in 2015.
But the former Tottenham man was at his dazzling best in Haifa, first assisting Aaron Ramsey to make it 1-0 shortly before the break.
Bale added the second with a stunning free-kick and rounded off the scoring in the 77th minute after Israel had Eitan Tibi sent off.
Unbeaten Wales subsequently leapfrogged their opponents to go top of the group, but Bale wants no let-up as they seek qualification to a first major tournament since 1958.
"We knew what a big game it was. A top-of-the-table clash and we don't often say that," he told Sky Sports.
"To come out on top is amazing. We're top of the league and we go on from here.
"The first half was hard and we did a lot of running. We closed them down well and the goal gave us confidence.
"We came out in the second half buzzing, we played good football and showed how good we are.
"We've put ourselves in a great position, but there's a lot of work to do yet, and all we can do is keep fighting and keep working hard."
One of the main plusses for Wales was the excellent combination work between Bale and Ramsey throughout.
Arsenal man Ramsey is now already looking ahead to what could be a crucial encounter against Belgium in June.
"We're where we want to be. We've had a terrific start to the campaign and we hope we can continue that," he added.
"We have a tough game against Belgium, but we're really looking forward to playing them in June."
