A common topic in alternate history fiction works is the question what would have happened if a major conflict had been won by the other side. These usually focus on the events after the conflict, and the change itself is not depicted in a realistic way: it's either not discussed, or attributed to a superweapon or deus ex machina.
I know that the Cold War was a complex time, with a huge number of social and economic factors in it so that there was not single realistic "miracle" which would have guaranteed a certain different outcome, therefore I list a number of disclaimers, in order to make this question fit into the topic of this site.
It doesn't have to guarantee a Soviet triumph, but it has to significantly increase its probability. A victory doesn't necessarily mean complete global domination. If the Soviet Union ends up in control over most of the Eastern Hemisphere, it would count as a victory for the Communists.
The change has to be a single event, or a collection of tightly coupled and interdependent events. It has to happen either during the Cold War, or not more than a few years before it. The Cold War should, at least in the beginning, look very similar to what happened in real life: the alliances should be roughly the same, the events like the war against Nazi Germany, the occupation of Eastern Europe, the Communist victory in China, and a cold war between the USA and the Soviets should occur (or at least begin), even if at different dates or different order. The major participants should be the same.
The change should have a realistic justification (so no secret Soviet UFOs), I would think in the following changes: events progressing slightly faster or slightly slower than in real life, a single large event or series of interconnected evens tilting history in the Communists' favor (if that had even a small chance of happening).
I'm thinking along the lines of the Soviet Union and its allies advancing faster against the Nazis and crushing them before the Allied landings in Normandy, or Stalin not butchering his officer class so they could respond effectively to the Nazi invasion right away, faster scientific development for the Soviets in electronics, computers, space, missile and nuclear technology, the Soviets invading Japan before the Americans can mount a Pacific campaign, no US intervention in the Berlin Blockade, Korea or Vietnam, or a different sequence of diplomatic events leading to Soviet domination in either Asia or Europe which in turn could lead to a victory on the other continent, etc.