Only Sergio Ramos remained from the Spain side that started against Albania, and the headline team news was an international debut for Las Palmas attacker Jonathan Viera. Illarramendi and Aritz Aduriz were also handed starts, as were Marco Asensio and Pedro in forward positions.
It was Spain that had the game's first shot on target in the third minute, but Israel goalkeeper Ariel Harush comfortably kept out a long-range strike from Asensio.
Almog Cohen hit one from distance in the 20th minute as Israel continued to impress, and backed by a vocal crowd, the home side were growing in confidence as the first period developed.
Spain had another half-chance just before the 30-minute mark when Aduriz met a high ball inside the Israel box, but his header was gathered by Harush, who was the busier of the two goalkeepers in Jerusalem.
Harush was again called into action in the 33rd minute to keep out a long-range strike from Ramos, before Asensio sent one wide of the Israel post in the latter stages of what proved to be a goalless first period.
Pedro had easily the best chance of the first half in the 43rd minute after being sent through by Viera following a quick Spain counter-attack, but the Chelsea attacker could not find a route past Harush.
Iago Aspas came off the Spain bench at the interval to replace Ramos, and there did seem to be more purpose about the visitors at the start of the second period, with Viera firing just over the crossbar after another slick move.
Israel were also threatening, however, with Hemed turning a low cross wide of Pepe Reina's post in the 49th minute.
Not too much happened in the 15-minute period that followed, with Israel holding firm in their defensive shape as Spain struggled to find that elusive pass in the final third of the field.
Aduriz should have netted 25 minutes from time after a low Asensio cross fell into his path, but the Athletic Bilbao forward somehow failed to make contact at the near post.
Spain came on strong after the introduction of Isco, with the Real Madrid midfielder injecting some much-needed quality into the final third of the field. Jose Callejon soon followed, while Benayoun was introduced for Israel.
It was the visitors that made the breakthrough in the 76th minute when Illarramendi's half-volley from distance flew into the back of the net.
Asensio thought that he had made it 2-0 in the latter stages after netting from close range, but the Real Madrid attacker was flagged offside as Illarramend proved the difference between the two teams on the night.