The Germans open their Euro 2012 campaign in Group B against Portugal in Lviv, Ukraine, on Saturday June 9, but after losing two of their last three games, Löw's side boosted flagging confidence against minnows Israel.
A first-half goal from Bayern Munich striker Mario Gomez put the hosts ahead before Leverkusen's Andre Schürrle came off the bench to double the lead eight minutes from time with a superb long-range strike.
Having suffered a shock 5-3 defeat to Switzerland in Basel last Saturday, the Germans managed to avoid their third straight defeat of the year, after also losing to France in February, but must still improve, according to Löw.
"It was a pretty decent final test, this will give us some momentum," he said.
"Not everything ran smoothly, but taking a victory into next week will do us good. We still have to improve and work on finishing our goal chances, the organisation was better, but there is still much to do."
Germany had far more shape and purpose in their attack than they showed in Basel, but captain Philipp Lahm succinctly summed up his team's laboured performance.
"We have sensational quality in the squad, now we just have to show it," he said. Adding, "we had some good combinations. It can't always go perfectly, which is why the victory was important.”
Germany's chances against Portugal received a boost with the news Bayern Munich midfielder Bastian Schweinsteiger should be fit for the opening game.
The 27-year-old injured his calf in Bayern Munich's Champions League final defeat to Chelsea a fortnight ago and sat out the win over Israel, but should be fit.
"Bastian has been pain-free since Wednesday," said Löw. "Now he has to start to run and he will train with the team again by Tuesday at the latest."
Schweinsteiger, who has scored 23 goals in 90 appearances for Germany, suffered heart-break in the final as his missed spot-kick allowed Chelsea to win the penalty shoot-out, but is one of Löw's first choice names.
Israel coach Eli Guttman is backing the Germans to live up to their pre-tournament billing as one of the favourites to lift the title in the Kiev final on July 1.
"I am satisfied on the whole," he said. "Germany is one of the best teams in the world, it was normal that we had to defend well against such an opponent.
"This German team are among the favourites, even their bench is impressive. They can certainly do it at the European Championships."