In a dead-rubber contest lacking entertainment on Monday night, Illarramendi provided a bright spark in the 75th minute.
The 27-year-old broke the deadlock when he met an Israeli clearance on the edge of the penalty area before driving a venomous half-volley towards goal.
Such was the technique of Illaramendi's strike that the ball ended up nestling inside the side netting.
Spain's 1-0 victory ensured they topped Group G by five points ahead of second-placed Italy.
Illarramendi is currently at Real Sociedad, where he is enjoying his second spell after an unsuccessful three-year stint at Real Madrid.
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