Was Stalin's persecution of his political enemies the most important factor that enable him to control the Soviet Union?

1. Stalin's exploit of the cult of Lenin.
2. Stalin's use of terror / His cunningness / Stalin's persecution of his political enemies

The Politburo was divided into two halves:
The Leftists (Zinoviev and Kamenev) wanted world revolution, and to abolish the NEP, but they hated Trotsky because they thought he was too ambitious.
The Rightists (Bukharin, Rykov and Tomsky) wanted to continue the NEP until the USSR was stronger.

Stalin played one side against the other to take power:
First, he allied with Zinoviev and Kamenev to cover up Lenin’s Will and to get Trotsky dismissed (1925). Trotsky went into exile (1928).

Then, he advocated ‘Socialism in one country’ (he said that the USSR should first become strong, then try to bring world revolution) and allied with the Rightists to get Zinoviev and Kamenev dismissed (1927). Stalin put his supporters into the Politburo.

Finally, he argued that the NEP was uncommunist, and got Bukharin, Rykov and Tomsky dismissed (1929).

Reference: http://www.johndclare.net/Russ9.htm

3. Unpopularity of Trotsky / Weakness of Trotsky

- Many in the party thought that Trotsky was too big-headed, and thus did not support him. Trotsky lacked supporters within the party as he was unpopular among the rest of the members.
- Secretary Stalin told him the wrong date for Lenin’s funeral, so he missed it – this made him more unpopular.
- Trotsky also wanted to try to cause a world revolution; many Russians feared that this would ruin Russia.
- Trotsky appeared less competent as he was only well-known for his achievements with the Red Army during the early revolution years and as a Commissar of War.

His unpopularity and lack of support within the party provided a stepping stone for Stalin to rise to power


Notes:
Compare and contrast Stalin and Trotsky
For a lot of extra detail, try the Wikipedia articles on the rise of Stalin, and Trotsky's fall from power.