First of all, make the Soviets disown any and all Azeri and Kurdish separatist movements after WWII and withdraw from Iran on time. That means their relations are preserved and any Irani leftist regime won't be inherently distrustful of the USSR. Secondly, have Mossadegh's reformist regime somehow survive the inevitable countercoup. That's not yet enough to pull the country into the Soviet sphere, since Mossadegh wasn't a big fan of the Soviets himself, but we can work from there.
The Tudeh Party of Iran can then try to pursue a "popular front" strategy, making a strategic alliance with Mossadegh and using the opportunity to establish more and more influence of its own in the country. Citing the threat of a monarchist uprising, they can demand more and more of a say in government while at the same time building a grassroots revolutionary base of its own covertly. When the Tudeh inevitably go far and break with Mossadegh, the Tudeh Party can make its move and try and take over, forcing the National Party out. This gives us... well, maybe not a satellite state, but someone who is friendly to the Soviet Union and dependent on them for survival. The British and Americans aren't going to let Iran get away easily, though, and they'll continue supporting the reactionaries - if it doesn't lead to another coup, then it may just lead to an early Afghanistan, writ large.