Interesting.
Rommel pushes all the way to Baku, eh? This would be difficult to achieve, even if he plows on through Arabia. The prospect of Germany fighting a war in the southern Caucasus against the Soviet Union is not as war-winning as one may assume. It might actually give the Allies who are sitting in Persia a task to do--namely strike the Nazis's flank. Assuming this occurs in 1942, then the German offensive into the northern Caucasus is just getting underway. If a large part of Rommel's army is isolated by the Persian attack, then there is a good chance that it would be surrounded and destroyed. Of course, knowing Rommel, he may attempt some wonderful campaign in the Caucasus mountains, eluding his pursuers in the hopes to link up with his only hope, the German Sixth Army . . .
just in time to be provide much needed reinforcements at Stalingrad. Nazis take the city, gain access to the Volga, and give Rommel another beautiful victory (though at this stage I am positive that Germany has already suffered irreparable losses).
But we can't forget the rest of Rommel's army, which when united was a terribly weak force. Now it is lacking the Desert Fox's leadership, and missing a large portion of its fighting force, conducts a fighting withdrawal back through Arabia. Reinforcements from India soon pour in, hastening the German withdrawal. The hypothetical commander of these troops,we'll say Von Arnim, lays out a defensive line at the Golan Heights. He is defeated like Rommel at El Alamein in OTL, and pushed across the Suez.
How's this? Note: I severely doubt the possibility of Rommel weaving his way around Soviet Divisions and mountain passes all the way to Stalingrad with a severely depleted force. I just included it because it seemed like it would be a fascinating idea----Rommel the Sherpa.