As far as "saving the world" goes, I think that's open to interpretation.

In terms of changing the course of the war, absolutely. The German High Command did not anticipate that the war in Russia would last as long as it did, and almost all of Germany's resources and troops were devoted to fighting on the Eastern Front, and stretched as thin as butter. The West was open to invasion, and by the time D-Day had happened and the allies grasped a solid access point to France, Germany didn't stand a chance. Hitler had two options: Keep everything devoted to the Eastern Front and get pummeled by the Western Allies, or allocate resources from the Eastern Front to the West and have a slim chance at fighting the Allies back while keeping the Russians occupied. The rest, of course, is history.

Even if D-Day were a failure, the Allies would have found a way onto the continent. The war in Russia was essentially doing all of the hard work for them. Had Germany not invaded Russia, we might be still seeing a Nazi Germany today in the modern era.