I'll argue that the United States didn't allow Russia to take Berlin -- it declined to even enter a race for the city.

For reading, I suggest Antony Beevor's Berlin: The Downfall and Cornelius Ryan's The Last Battle. I'll also recommend "The Fall of Berlin and the Rise of a Myth" by Donald Shepardson.

The short of it is that there's two schools of thought on this. One theory, that put forward by Ryan in 1966 with his book, is that Eisenhower failed to see that the war had turned into a political struggle with the Soviet Union and that the disorganized Germans were just waiting for an opportunity to surrender to the United States. The counter view is that Eisenhower's move was the correct one and saved thousands of American lives for territory that in the end would be turned back to the Soviet Union anyway.

Let's look at it from the standpoint of pure timing. Parts of the 2nd Armored Division of the 9th U.S. Army reached the Elbe River about 50 miles from Berlin on April 11. East of Berlin on that date, the Soviet Army was preparing to launch the final offensive that would encircle the city. The Battle of the Seelow Heights, the last defensive line before Berlin, would not begin until April 16, but the Soviets were already moving soldiers into position. By April 19, the Seelow Heights had been taken. By April 23, Berlin was encircled.

Gen. Simpson, commander of the 9th Army, expected to begin a drive to Berlin. "My people were keyed up," he told Ryan. "We'd been the first to the Rhine and now we were going to be the first to Berlin. All along we thought of just one thing -- capturing Berlin, going through and meeting the Russians on the other side."

But on April 15, Eisenhower ordered him to stay put. Maj. Gen. Raymond McLain, corps commander of the 19th U.S. Army Corps, was later to say that he believed it would have taken his corps no more than six days to drive to Berlin.

Is that possible? Tough to say. The advancing Americans were strung out, with their logistics stretched. Even Ryan describes how the advancing units needed to stop for maintenance and regrouping. Furthermore, the advance left dangerous pockets of resistance behind. Trailing units frequently found themselves in firefights after advancing units accepted the surrender of a town. Holdouts, it seemed, needed time to realize that the Americans were at their doorstep.

Even if the U.S. Army reached the gates of Berlin, then what? It certainly lacked the manpower at the front to "take" the entire city; the Soviet Union suffered more than 80,000 killed and another 250,000 sick or wounded during the battle for Berlin; at best, the United States could have contributed to the fighting in Potsdam and some western neighborhoods.

Eisenhower directly believed that capturing Berlin served no great strategic purpose, and never even planned to capture Berlin.

By 1945, U.S. manpower was beginning to fall short in trained soldiers, and the logistics were simply not there to push into Germany. Additionally, the Western allies felt that it was strategically more valuable to cut the Leipzig-Berlin line to reduce enemy logistical capabilities, and to cut off German forces in Italy from being able to move into Germany to bolster defense of the home country.

You can read about the strategic planning of the Allies at the Yalta Conference, here.