The three-time European champions, among the title favourites, dominated with a performance that was a marked improvement on their 5-3 defeat by Switzerland on Saturday.
However, they wasted close to a dozen clear chances on a rainy evening in Leipzig as they prepare for the finals being co-hosted by Poland and Ukraine.
Germany face Portugal on June 9 in their first match in Group B which also includes Netherlands and Denmark.
"We can say this was a decent final test of our preparation and will give us a bit of a boost," said coach Joachim Low, who is leading Germany for a third major tournament.
"Obviously not everything worked well yet. It is clear we could have scored more goals but to go with a win into next week is good for us," he told reporters.
"We will improve, the tempo at the tournament will be higher, in the second half we squandered six or seven chances... so there is still a bit to work on."
With Bastian Schweinsteiger ruled out with a nagging thigh injury, Toni Kroos partnered Sami Khedira in a holding midfield role.
POURING RAIN
Captain Philipp Lahm switched from his usual right back position to left-back with central defender Jerome Boateng playing on the right where he is less comfortable.
The Germans, as expected, took the initiative in constant pouring rain but had to wait 20 minutes for their first clear chance when Boateng rattled the post with a curled left-foot shot as Israel defended in numbers.
Gomez broke the deadlock five minutes before halftime, picking up a Thomas Muller pass in the box and firing high into the net for his 22nd international goal in 52 appearances.
Germany goalkeeper Manuel Neuer was called into action twice soon after the break to rescue the hosts before they upped the tempo again, missing several chances with Lukas Podolski and Mueller among the culprits.
Substitute Schuerrle grabbed their deserved second goal eight minutes from time, rifling home from 20 metres as Germany won their first match this year after two defeats.
"We had some good combinations, allowed nothing to happen at the back," said Lahm. "We [Bayern players] had not played for 12 days, we had only three days of training with the team so not everything can work instantly. That's normal."
"We'll be fully fit when the tournament starts," added Lahm who along with his club team mates had been given some rest after losing to Chelsea in the Champions League final.
