There are numerous ways in which the Mongols were able to maintain control of their empire. (But please recognize that they did not keep control of it for very long -- they didn't even manage 200 years of rule).
Here are some ways that they managed to keep control:
- Fear. The Mongols conquered through use of fairly brutal means. Their subjects knew (or feared) that the same brutal tactics could be used against them if they rebelled.
- Use of local elites. At times, the Mongols would use local elites who were relatively happy to maintain their position in society, even if they had to carry out Mongol orders.
- "Divide and rule." They would often play various local groups or classes off against one another. They would favor Group A and Group A would know that their power depended on the Mongols so they would serve well.