The 1223 battle in which Mongol generals defeated a Rus'-Cuman coalition was the Battle of the Kalka River. It was fought on 31 May 1223 in what is now Ukraine, during a long Mongol reconnaissance campaign west of Central Asia.
The Mongol force was led by the veteran commanders Jebe and Subutai. After campaigning through the Caucasus and defeating the Cumans, they drew the pursuing Rus' princes into a feigned retreat. The Rus' and Cuman armies crossed the Kalka River without maintaining a unified command, allowing the Mongols to strike their separated formations.
The coalition included forces from several Rus' principalities, including Kiev, Galicia-Volhynia, Chernigov and Smolensk, alongside the Cumans led by Khan Köten. The defeat was severe: many princes and thousands of soldiers were killed or captured, while Mstislav the Bold escaped with part of his army.
A common mix-up is treating Kalka as the beginning of the full Mongol conquest of Rus'. It was an early warning and reconnaissance victory; the major invasion came more than a decade later, when Batu Khan's armies conquered much of Kievan Rus' between 1237 and 1240.