Having suffered a shock 5-3 defeat by Switzerland in Basel last Saturday, the Germans managed to avoid their third straight defeat of the year, having also lost to France in February, in their final EURO 2012 warm-up match.
A first-half goal from Bayern Munich striker Mario Gomez put the hosts ahead before Bayer Leverkusen's Andre Schuerrle came off the bench to double the lead eight minutes from time with a superb long-range strike.
But there was little else to cheer German fans on a damp night in Leipzig and captain Philipp Lahm succinctly summed up his team's performance: "we have a sensational squad, we only need to show it."
Germany coach Joachim Low was happy with the victory, even if his team failed to impress in front of goal. "That was a decent final test for us, it will give us some momentum," he said. "Not everything ran smoothly, we could have done with more goals, but the victory is good for us. The organisation was better than against Switzerland, but there is still work to do."
Having fielded an experimental team in Basel, coach Joachim Loew opted for a side which is more likely to start the opening EURO 2012 game against Portugal on 9 June in Lviv, Ukraine.
Vice-captain Bastian Schweinsteiger, missing his sixth straight international and nursing a calf strain from the UEFA Champions League final, was the only noticeable absentee as seven Bayern Munich stars started for Germany.
"Bastian has been pain-free since Wednesday," Low told German television. "Now he has to start to run and he will train with the team again by Tuesday at the latest."
Schweinsteiger's club team-mate Toni Kroos slotted into the midfield defensive role alongside Real Madrid's Sami Khedira as the hosts spent the opening 20 minutes camped in the Israel half. Gomez tested Israel goalkeeper Ariel Harush early on and defender Jerome Boateng hit the left post with a well-timed shot.
The heavy rain affected the game's tempo and it took a clever pass fromKhedira which eventually landed at Gomez's feet for the Bayern star to fire home and break the deadlock on 40 minutes.
After the half-time break, Israel coach Eli Gutmann made three changes, including bringing off captain Yossi Benayoun of Chelsea. It was replacement Gil Vermouth who first tested German goalkeeper Manuel Neuer with a well-timed drive on 54 minutes which the Bayern star had to tip over the crossbar.
It proved to be the wake-up call the Germans needed as Arsenal-bound Lukas Podolski found plenty of space down the left flank and looked increasingly dangerous, before making way for Schuerrle on 66 minutes.
With a quarter of an hour to go, Bayern's Thomas Mueller wasted a golden chance to make it 2-0 when he fired wide with scarce pressure from the tiring guests' defence. Schuerrle made sure of Germany's win when he unleashed a fierce drive which gave the Israeli goalkeeper little chance on 82 minutes.
But with the Portuguese, FIFA World Cup™ finalists the Netherlands and Denmark awaiting them in Group B at EURO 2012, Germany can expect much tougher challenges in Ukraine and Poland.