Captain Davis lashed home a powerful effort with 18 minutes left, responding to Eden Ben Basat's headed opener just before the break.
A share of the spoils represented a fair verdict - and a surprising one given Northern Ireland's form and depleted numbers - allowing Michael O'Neill's men to banish at least some of the scars accrued during defeats to Luxembourg and Azerbaijan.
Davis, after a hard first campaign as skipper, was also fully deserving of a leading role and a fifth international goal.
Just four days after abandoning his favoured 4-2-3-1 formation for 3-5-2 in Baku, O'Neill reverted to type.
Personnel-wise there were no fewer than six changes, half unavoidable due to suspensions for Jonny Evans, Gareth McAuley and Oliver Norwood.
O'Neill's decision to voluntarily leave out another of his senior men in Chris Brunt - stood down alongside Shane Ferguson and Jamie Ward - may have raised eyebrows but the return of the rock-solid Chris Baird and Sammy Clingan in midfield ensured there would be no lack of experience.
With Ward warming the bench it quickly became clear that Davis would be Martin Paterson's main attacking support, the Southampton midfielder handed a more advanced role after several matches in the engine room.
Northern Ireland's early strategy involved balls over the top for Paterson, who made a half-hearted penalty appeal after nine minutes when Dudu Aouate challenged him for Baird's chipped pass.
In the 19th minute Corry Evans crumpled after both he and Sheran Yeini slid to retrieve a loose ball, making way for Brunt's belated arrival.
He had been on the pitch a matter of minutes when he collected Davis' lay-off and shot a yard over from outside the area.
Israel spurned a presentable opportunity of their own when McArdle's defensive header found Lior Refaelov lurking on the right but his first touch was with his knee and the ball bobbled out of play.
In the 33rd minute a back-tracking Niall McGinn found himself needing to make a crucial tackle on Eyal Meshumar as he homed in on goal.
The Aberdeen winger would not be anyone's first choice for such a task but he managed to muscle out the full-back without attracting the referee's attention.
From then on Israel were well on top, Roy Carroll awkwardly saving a Bebras Natcho free-kick with his feet then coming to collect a bouncing ball at the edge of his area only for McArdle to get in the way and leave him stranded.
Cathcart was on hand with a sliding block to prevent Ben Basat taking advantage of the unguarded net but he did not miss his next chance.
Meshumar was proving a constant threat down the right and and it was his cross that allowed Basat to head home from eight yards.
Carroll was rightly upset to see the striker nip between both centre-halves in order to do so.
Five minutes into the second half a clash of heads between Cathcart and Keinan left both men bleeding, though the Blackpool man at least earned a rare corner in the process.
Paterson was the target but he could not get a clean connection.
Clingan, putting in a highly impressive shift, got back well to mop up a dangerous ball at the opposite end but his side needed some attacking spark now too.
Davis attempted to supply it when he shook off Yeini and let fly but his shot flew just wide after a slight deflection.
Ward replaced the quiet McGinn with 25 minutes remaining and instantly brought some energy to proceedings.
The equaliser came after O'Neill had gone back to 3-5-2, Clingan putting a foot in to regain possession and begin a new attack.
Ward spotted the well-placed Davis arriving at the edge of the area and he buried a first-time that was left Aouate grasping at air.
Northern Ireland were energised, Ward shooting wide seconds after the restart and Paterson's volley beaten clear by the goalkeeper following Brunt's clever chip.
It was a wonderful chance but Aouate's reflexes matched the finish.
Hodson, given licence to attack now, hesitated when Davis' header seemed to put him clear on the right and from there on Israel were in the ascendance.
They camped out in Northern Ireland's final third but a series of tackles, blocks and clearances ensured a deserved point.