There's no saving Japan after Pearl harbor.
Germany on the other hand had a pretty plausible shot at sticking around. Say Hitler launches Barbarossa in the spring of 1943 instead of fall, without redeploying to make sure Yugoslavia and Greece were secure. That gives Hitler plenty of time to overwhelm Russia before winter sets in, although since Stalin was even les convinced of Hitler's treachery then, Russian defenses would be farther inland in more defensible positions, instead of on the border, awaiting invasion. It's unlikely Russia would have been completely wiped out, and all Hitler really cared about in the immediate future was the area west of the Urals. So Russia may have lived on out of sheer compromise with the very busy Nazis, but definitaley in a diminished form, certainly without Ukraine and the oil-producing south.
Of course, it helps drastically if Hitler doesn't declare war on the US for no strategic reason (after Pearl Harbor) other than he'll be fighting us eventually.
With the US soley focused on the war on Japan and all, that has huge repurcussions on the western front. Without the
US to take some pressure off Britain, the Soviets would be in even worse shape in that they aren't getting even meager supplies from the Allies (need them for themselves even more!) and Russia is utterly isolated. The American public is still vastly isolationist, and after a two year war with Japan, they aren't going to be willing to jump into another one with an even stronger foe. Similarly, even MacArthur wasn't for Operation Unthinkable in OTL. The fact that Hitler didn't bring the war to America made America's real enemy (Japan) completely seperate from the potential enemy. Basically Americans will see one world war as good enough, and retire to fight another day.

So with no D-Day, and some sort of German victory in the east, Germany pushes Britain and the Commonwealth out of North Africa, and the US probably won't intervene directly until either an invasion of Britain (still highly impractical) seems imminent, or the Germans continue the push towards the Middle East, controlling a vast supply of oil. Especially if there is a more war-weary US (Japan may have seized Vladivostok and substantial oil supplies in Siberia after Russia's collapse, like they did with France in Indochina, letting them stick around longer), American might not even go to war with Germany until they invade India and it looks as though they might conquer the whole world. All this is highly unlikely, because Truman (and even more so Roosevelt) would know better to delare war on Germany because they'd be the enemy in the long run. So to make it work you need a isolationist president, popular with the people and can override congress. Either by the president's death or a suprise election, Roosevelt's successor will focus on Japan and the Great Depression. But any president would know that something like the Cold War would be brought on with Germany, except the Nazi were smarter, more industrialized, and crazier than the Soviets ever could have been.
So what's the Axis' best shot? Japan had no shot. So what I've come up with to make Germany happen (at least for a while, they can't keep up with the Allies in the long run).
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Earlier Barbarossa. Italian troops pull out of Africa and lay claim to "Dalmatia". Italy gets invaded later, no big deal, not a serious threat to Germany anyhow (Peninsula campaigns are never fun).
-Even though this "no winter" Barbarossa is about as big of a gamble as the one in OTL, it ultimately leads to a
German "victory" in the east, albeit immense military casualities, both sides. Russian rump state formed, a few miles west of Moscow's remains is the western border, or alternatively just over the Urals.
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Hitler doesn't declare war on the USA. Of course embargoes will intensify until the fighting begins.
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War weary US. Nobody wants a world war with Germany after an attritous war with Japan. Just ask Russia.
And that's pretty much it.
Pretty plausible, eh? Although that still is full of holes...which I may correct later.

Feel free to poke more.
Alternatively, Hitler doesn't dismiss his nuclear bomb research as 'too ambitious' and gets the bomb sometime before 1944. London, Moscow, both the Dictator'grads and many others get decimated and eventually the Amerikabomber shoots down eastern seaboard cities. America retaliates by devastating Central Europe with bombs, and everyone dies. But I don't like that scenario as much. 