Not by cracking Enigma?
http://en.wikipedia.org/wiki/Cryptanalysis_of_the_Enigma
And remember, "the war" was also being fought in the Pacific, also with a spectacular imbalance in cryptology strength between the Allies and the Axis.
http://en.wikipedia.org/wiki/Japanese_naval_codes
http://en.wikipedia.org/wiki/Magic_%28cryptography%29
In general, code-breaking had a lot to do with the outcome of the war.
From his wikipedia article: He died during an inspection tour of forward positions in the Solomon Islands when his aircraft (a Mitsubishi G4M "Betty" bomber) was shot down during an ambush by American P-38 Lightning fighter planes. His death was a major blow to Japanese military morale during World War II.
No, not by cracking Enigma.
Enigma didn't result in 750,000 casualties and 900 Aircraft losses. Stalingrad did.
Enigma didn't result in the loss of the Sixth Army. Stalingrad did.
Enigma didn't change the scenario from Germany controlling all of Europe and its resources to playing defense from two sides. Stalingrad did.
For all the bravery and blood shed by the red army, their winter is the thing that changed the outcome of the battle. The winter forced a halt in the German advance, allowed the Russians to regroup and was the number one casualty producer for the nazi's.
I don't undervalue the contribution code breaking made to that war, but there was only one turning point, and it came , very clearly, in Russia.
I do agree that brainpower won the war - our cryptology was stronger, resource management between the Pacific and European fronts was superb, and the Allies had a knack for picking battles and battlefields where they could excel
If America's leaders had done everything wrong, they would have ended the war without big territorial gains for their side, with a negotiated peace leaving Japan in control of Asia. (That, by the way, is exactly what Japan's leaders got wrong from the strategic point of view. They really believed before the war started that that was a likely outcome of the war. They didn't count on the Allies insisting upon unconditional surrender after the sneak attacks on Pearl Harbor and Singapore.)
They were saved from their mistakes by superior equipment (especially aircraft) and eventually better and more experience personnel. They didn't start tactically winning battles until well into the Pacific Campaign.