Aaron Ramsey opened the scoring just before half-time after latching onto Bale’s flick to loop a header into the back of the net.
Bale doubled his side’s advantage minutes after the break, placing a superb free-kick over the wall and into the top corner.
Israel’s task became even harder when Eitan Tibi was sent off after picking up two yellow cards in as many minutes for two fouls on Bale.
The Real Madrid man picked himself up to round off the socring in the 77th minute, smashing Ramsey’s pass into the back of the net to end Israel’s perfect record and move two points clear at the top of Group B.
Wales started what Coleman called their biggest game since their Euro 2004 play-off defeat to Russia in 2003 brightly, with Ramsey and Bale both missing the target with early shots on goal.
Bale, who has received plenty of criticism for his performances for Real Madrid in recent weeks, was a constant threat to the Israel defence and created a brilliant chance for James Collins.
Minutes earlier the West Ham defender was in the right place at the right time to head Tal Ben Haim’s dangerous cross clear, but with the goal gaping at the other end he could not steer Bale’s cross into the net.
The home side just could not get going in attack as Tibi’s poor pass allowed Bale to drive into the penalty area, but his shot was blocked by defender Tal Ben Haim.
Wayne Hennessey was called into action for the first time midway through the first half when he pushed away Eran Zahavi’s shot, but that was the only time the hosts threatened his goal in the first 45 minutes.
Israel were handed a setback when Omer Damari, who is Group B’s top scorer with five goals, left the field through injury, forcing a change with Tomor Hemed coming on.
Eli Guttman’s men received a further blow when they failed to deal with a long, hopeful ball from Hennessey which Bale flicked on to Ramsey, who looped a header over Ofir Martziano to give his side the lead seconds before the interval.
Wales started the second half in much the same vein as the first and they were rewarded when Bale, who was fouled by Tibi on the edge of the box, pick himself up to lift the ball over the wall and into the back of the net.
Tibi, who received a yellow card for the foul, was show red a minute later as he picked up a second booking for another foul on the Real Madrid forward.
Coleman’s men were dominant as first Bale, and then Hal Robson-Kanu, tried to extend their side’s lead but both efforts failed to test Martziano.
Israel sent on former Chelsea youngster Ben Sahar as they desperately searched for a way back into the match and he produced his side’s best moment of the second half, but Wayne Hennessey produced a smart save.
But Bale put the result beyond doubt as he raced onto Ramsey’s perfectly-weighted pass to find the net and hand Wales their first competitive away victory against a top-50 ranked side in eight years.
Coleman’s men will be top of Group B until at least Tuesday when either Israel or Belgium could have the chance to reclaim their place at the summit.
Wales are next in action when they welcome Belgium to the Cardiff City Stadium on Friday June 12 as their bid to qualify for their first European Championship – and their first major tournament since 1958 – continues.