The first thing is that they were absolutely not "unruly." The Mongols as a military had a remarkable discipline. To read accounts of their battles demonstrates exactly how ordered they were. And that also expanded to their civic laws. The Mongols had a very defined legal code. They even developed a postal service. To think of them as disordered barbarians gives the wrong impression. They were brutal. They were merciless. But they weren't disorganized.

Second, is that they were led by an fantastic general in Genghis Khan. And he recognized and encouraged brilliance wherever he saw it. When an enemy shot his horse out from under him, he made that enemy a sub-general. When he found a great Chinese or Persian administrator he kept them around. Everyone had a chance to rise in the empire. And no one was safe. If you screwed up or betrayed the Mongols, punishment was swift and severe. That tended to encourage competence and even greatness throughout the ranks.

Third, they may have had the best pre-modern intelligence service. Genghis was usually well aware of what was happening in neighboring countries. When nations had religious turmoil, his spies were there to proclaim that the great Khan was a believer in religious freedom. When mixed forces faced the Mongols, it wasn't at all unusual for the Mongols to bribe one group to betray the others. And they usually knew very well which commander in an opposing force might be susceptible to such things. Knowing when and how their enemies were weak made the Mongols effective.

As part of this they also had an excellent scouting force. Their light cavalry was as good as any in the world at the time. And because of their discipline they could be counted on to keep to scouting. So they pretty much always knew where the enemy was and what they were up to. While most opponents rarely had any idea where the Mongols were. This allowed the Mongols to frequently choose when, where, and even if a battle took place. One example of this is the Battle of the Kalka River. Where they lured the Russians into a prepared battlefield. And did so in such a way that the Russians arrived strung out in a long disorganized line. Thus a fresh prepared Mongol force hit a tired disorganized force many times their size and wiped them out.

Fourth, because the Mongols usually operated as an all mounted force, they were fast. They could seemingly show up anywhere. And sometimes seemed to be everywhere. Even their baggage train was usually horse mounted. This gave them both strategic and tactical advantages no one else at the time could match. More than one battle was won because a force of Mongols showed up somewhere faster than another army should have been able to.

Horse archers in general are terribly difficult for other armies to deal with. The Mongol bow outranged most other bows. So they could shoot at infantry without consequence. And even other horsemen generally couldn't catch them, but while they were trying the Mongols could pepper them with arrows.

Fifth, the Mongols were actually great at siege warfare. One standard tactic for dealing with nomadic horse tribesmen was to sit behind fortified walls. But the Mongols learned siegecraft early in China. Not only could they build advanced trebuchets and the like. They may have even started using cannons. They may have introduced gunpowder to Europe and the Middle East. But they absolutely used them in China. There were a lot of cities that had withstood sieges before, that the Mongols were able to batter down the gates or walls.

Sixth, they were brutal. If you cooperated they would conquer you and incorporate you into the empire. If you didn't things were going to go very badly for you. Many towns were killed to a man, woman, and child. In one town they even went so far as to kill every cat, dog, cow, sheep, etc. as well. And they were ruthlessly efficient about it. Instead of just tearing through a town they would go through it methodically and then each soldier would be assigned a duty to kill so many. And he would report back with a bag of ears to show that he had done his duty. Then they would ride away, wait a few days and then return and kill any survivors they found. When they said kill everyone, they meant it. And this tended to encourage a lot of towns to surrender. Another result of the discipline they had.

Simply put they were highly disciplined and excellently led. They generally knew how to best hit their opponents and had the skills and technologies to do exactly that. And they combined this with a casual disregard for human life and a belief that they had a divine mandate to conquer the world.