Kotkin's Stalin biography gives a couple of answers to this. One was that as General Secretary, Stalin was in a position to do a lot of business with the security apparatus. Another was simply that Stalin was reasonably close to Dzerzhinsky, both being close to the centre of power during the revolution. Finally Kotkin suggests that Stalin cultivated Dzerzhinsky's immediate subordinates (Menzhinsky, Yagoda) as a backup plan. After all Dzerzhinsky had other work to do so he wasn't actually available all the time. It also follows a pattern Stalin appears to have used in other ministries, where he cultivated more than one contact so as to have two sources of info, play them against each other etc.

By comparison Trotsky and Zinoviev had few if any of these advantages, and didn't seize them when presented.